This answer is rooted deeply in the principles of the specific Old School playstyle that the question is about, and which loosely define the OSR movement.

By making mapping a part of play, you can both increase engagement with the mapping, make the time spent mapping less separate and more overlapping with the “interesting” things, and decrease the absolute amount of time spent mapping.

But how do you make mapping a part of play?

The 1^st correction: don't give mapping descriptions on sight

Mapping takes time. And I don't mean out of game; mapping takes time in-game in an OSR RPG. That means that proper (i.e., accurate, detailed) mapping can't be done just by glancing into a room. If you're giving foot-scale dimensions as soon as the party opens a door, stop. Give them a visual impression of the room, not a mathematical impression of the room, and keep play going.

Which leads to…

The 2^nd correction: don't give away mapping information for free

Mapping is work. The mapper doesn't just glance around and start drawing a grid-perfect map. Accurately mapping a room or corridor involves pacing off the distance or getting out a knotted rope that's brought along just for the purpose. The party mapper measuring and mapping a room is as much legwork and moving around as the party expert/thief searching for traps or the party elf combing the stonework for secret doors.

Just like you don't give away the location and nature of traps and secrets just for the asking, don't give (accurate) mapping information just for the asking. When the mapper asks how long the corridor is, ask them if they start measuring it by slowly pacing down the corridor. At first you'll get a panicked reaction “No!” as they envision their doom in pit traps and on the blades/fangs of lurking beasties, but after a few repetitions of requiring the mapping character to actually acquire their desired map data in a real way, they'll start getting choosier about when and how they seek that data.

Maps and map data are a resource, and like every resource in and OSR game, the game kind of breaks when they're still required but made freely available.

You'll find that the mapper doesn't try to map rooms on sight anymore; they'll wait until a room is somewhat explored first. You'll find that mapping becomes the answer to “and what are you doing while those two spend three Turns checking the walls for secrets?” and begins to naturally overlap with such activity.

You'll also find that the mapper acquires the information more organically, making the process more part of the in-game activity itself than dry bookkeeping at the table. This in turn makes mapping information clearer, since the character is directly engaging with the dimension of the territory they want to record: if the mapper asks how wide the room is, ask them how they measure it; if they say they pace off the wall that the door they came in through is in, that's a mental image of activity and exploration happening, not just dry at-the-table bookkeeping. If they want to know how long the room is, they similarly have to choose the wall to pace off.

All that moving around the room is also in-game activity that can interact with the ever-present Unknown of a dungeon, which keeps the tension a bit higher than your average bookkeeping.

Does that sound tedious? Well that's actually a feature and self correcting, because…

The 3^rd correction: don't assume mapping will happen

Mapping is something the players elect to do because it has utility — it is a resource they should be managing, not you. Don't assume or guarantee it for them!

Making mapping an in-game activity moves it into the realm of player responsibility. They want a map? Then they have to do the work to make the map. They don't like how long the mapper is taking to have their character strut around the room? Let them debate amongst themselves whether to make it stop or grudgingly put up with it for the greater good, instead of resenting you for the time it takes. Let the players choose to forego an accurate map!

Really, often they won't need an accurate map. The optimal behaviour is to map only as often and in as much detail as is necessary to be able to safely and quickly navigate around and back out of the location, and sometimes that means a boxes-and-lines map is good enough. How and what they map should be theirs to determine and devise. When you make that decision for them, all those times when the detail is unnecessary are, well, unnecessary, and turn the map into an imposition by you on them.

Let the players self-regulate mapping duties and game-time. When they really do want a good map, they'll invest their efforts into making one!

The challenge: refocusing on visual descriptions

The habit of initially describing rooms for the benefit of the mapper is a hard one to break. You might not be doing this to the extreme I'm about to depict, but the basic principle is the same regardless of degree: describe for the eyes of the adventurers and the mind's eyes of the players, not for the map of the mapper.

It's easy to say “it's a 20 by 20 room with a well in the north-east corner”, but that ease is like candy: it's tempting in direct proportion to its unhealthiness for the game. Save that kind of information structure for when the mapper has said “I spend a turn measuring and mapping the room while the fighter binds the wizard's wounds” or whatever. Toss those description habits and develop eye-view description habits:

Stepping up to the arch, your torches reveal a dead-end room. It's twice as wide as the corridor you stand in and square, with no other visible exits. In the far right corner is what looks like a low circular wall surrounding a pit or well.

The temptation is to info-dump, I know, but keep it simple to the point of actually missing details, and focus on suggesting a broad-brush impression of the room. This keeps it digestible and gives the players something to engage with and explore. It's a first visual impression for the adventurers, after all, so brevity is fitting anyway. As is usual in OSR games, the players will ask questions about features' details, which is akin to their character turning their attention onto the features within the game. (“What kind of wall is it?” “It's rough masonry, knee-high, and moss grows in the cracks.” “I walk over and hold my torch up to look into it…”)

And as more-or-less implied previously, if the mapper wants to map, using visually-focused descriptions makes acquiring mappable details just a different kind of question and detail that the player asks and their character inspects, instead of a separate category of table activity.

As a bonus, giving visual descriptions dovetails with the 1st, 2nd, and 3rd corrections: if the mapper or party wants a map faster, they can make a rough one based on the not-very-accurate idea of the space they get from the visual descriptions. There's no need to switch to Mapping Conversation Mode with you — they gather the details they want (if any) via exploration and your descriptions in response, seamlessly as part of normal exploration play.

Summary

Don't give the map details away at a glance, because you want the mapper to be acquiring this stuff through active interaction with the in-game environment, in a way that overlaps with and interacts with the other PCs' explorations and activity, and in a way that makes it the players' collective concern to manage and choose to do or forego instead of yours.

Give visual descriptions focused on what it would look like standing in that place, instead of descriptions tailored with a mapper in mind. Let the players drive the mapping, and let them do as much or as little as they all want. Let intra-party pressures determine the level of detail or lack thereof that they (collectively and emergently) decide is good enough for their maps.

P.S.: Don't forget the paper and ink

And it goes without saying that they can only map if they have the means and supplies. Don't give them maps for free in money or planning terms either! If they want a map, let them plan for it and buy paper, ink, quills, and ways of keeping them (and the resulting maps!) safe from unexpected tumbles into underground waterfalls.

Or not — again, it's up to the players now whether they want good maps or not.

Drop formal mapping by the players from the game, if the process of mapping in details is getting in the way of fun. OSR games do not mean you have to sacrifice your fun, and though it is realistically "old school" to get out the graph paper and describe the turns of every wall to the designated mapper, it is equally accurate (at least from the early 1980s when I started playing basic and AD&D) to play these games eschewing maps altogether.

So if the group just isn't into the accurate player-made map approach, agree an alternative, such as:

1. A character is making a map (and must have necessary equipment listed). But there is no need to act it out in detail, because it is actually a boring chore that enables safe exploration, not the fun part of discovery and adventure.
2. Assume the PCs are good enough at navigating in most scenarios that they can just say something like "We go back the way we came to the room where we defeated the gnolls" and you cross off the necessary time. This may be slightly unrealistic, but getting lost in the distance between a dozen rooms is rarely an interesting story.

You can switch between the two with fair warning, such as "these twisting caverns are too complex to just remember, if you don't have someone mapping them there is a good chance you will become lost".

The challenge then becomes how to get players to visualise the same layout in case it becomes important.

• For battles I would suggest you sketch the local area at the start. Sketch definite encounter areas in advance to just put down at start of the fight.

• For outside of battles I would suggest a lightweight version of your current explanations, and just live with the fact that sometimes players will misunderstand and need things explained a second time if they get confused or make weird decisions. If something is going to be too complex to put in words, again a quick sketch of just the room shape, entrances and exits is probably all that is required.

In nearly every game I've played, we've solved this problem by having the DM draw the map for the players.

Sometimes the map is much larger than the battle mat. The solution we use is to have an exploration map -- basically a blank white piece of paper on which the DM draws the map freehand -- and then, when combat happens, the DM draws the room(s) containing the combat onto the battle mat.

You've noted that having the DM "draw difficult rooms out" takes about as long as describing them, and is boring for the players. I'm not sure why this is happening. Do you have a lot of intricately-drawn rooms where nothing important happens? If the DM just draws a highly-simplified version of the room onto the exploration map, and gives the interesting parts of the description verbally, that might solve your problem. (And you can still draw the full version of the room onto the battle mat if combat breaks out.)

In some games, notably Pathfinder Society games, I've seen DMs draw all the important maps onto battle mats before the game starts. This has never seemed great to me, because it only works if we're railroaded into those specific battles, but it's worth thinking about at least.

The group I play with has tested multiple methodes for maps.

Pre-drawn maps

Important locations that will probably be visited can be prepared in advance. This way it takes no time to get the map ready. If you explain each room as they enter, you split the explaining time up with suspense, exploring and possibly combat.

Bonus tricks:

1. You can tape the paper together to make a sturdy map. This does give away the general shape of the map. For buildings, this usually is apparent from the outside. Use paper to hide unknown parts.
2. But the maps on scrap cardboard and cut them out per room. This way you don't have to hide other rooms, just line-of-sight if you want to.

Computer aid

The same can be done on the computer. We used Roll20 together with a projector to show the maps. Maps are pre-loaded before we start by the DM and he can control a fog of war to hide everything we don't see.

Bonus tricks

1. Large TV's work just as good.
2. Figures of monsters/NPC's can also be loaded to easily show all without having to hide a name in a book.

Miscellaneous

1. You can prepare generic battle maps for random encounters. This gives you a lot of time to design good maps, but it does not take game time.
2. Keep your maps simple if they don't like the time it takes. You can also but details behind checks (spot/perception/search/investigate). With multiple DC's you can hide basic information behind the question "Do you wan't to look around in the room?" If they just want to pass through, they don't get the info.

In the time before time, there was a text-based video game called "Zork". Every solution I found to zork was mapped with boxes and lines connecting these areas. Examples Here This makes for a great quick and dirty mapping style for the player characters to employ. You get the basics of the room and how it relates to other areas.
Players can take quick notes about the rooms i.e. "found well", "spider statue" or "blood altar", basics about the rooms that might be useful if there is a need to backtrack or retreat.

Larger tactical maps should be pre-drawn by the GM and made available to the players as required.

SevenSidedDie had some great reasoning behind why players or characters wouldn't be measuring out paces for rooms and detailing much of it.

Although not specifically a tool for the mapping aspect of an OSR game, I have found a useful technique that can be incorporated into this, because the crux of the problem is the constraints of verbal communication.

I often find that it is necessary to communicate detailed information to a single player, and that this activity is typically a disruption of play, because it isolates the other players. It becomes a bigger interruption when I need to do separate individual messages to several characters.

My resolution was to go through my notes and prepare communication shortcuts on cue cards. Every time I found a piece of information that only a single character will utilize, I put it on a card, and when a character accesses that information in play, (in your case, by mapping out a room) I give them that card and resume talking to the group, telling everyone the generic information. This allows me to metaphorically have "multiple voices" while running a game.

So, you might have cue cards with room dimensions, or even small drawings of single rooms or halls, if you can find graph-lined cue cards. While you describe the crumbling walls and mildew stench, hand the mapper the matching cue card when he goes to do his work.

When I’m the mapper, I use the box-and-lines method that JPicasso mentioned.

When I’m DM... I’ve had players who don’t do well with only verbal descriptions. They need visual aids. So, I’ve had to adjust. I use Encounter Elements or Dwarven Forge Game Tiles (just the basic ones) or Blue Dungeon Tiles to quickly show the general layout of the area the PCs can see. When they move, I deconstruct the areas they can no longer see and construct the areas they can now see. All of these aids make this quick enough to do on-the-fly. (And I’m constantly looking for other options.)

Not only does this help any mapper, it also helps the the whole group visualize the space.

when I describe even the simplest room dimensions and exits to the party's mapper, the other players lose interest.

Why are you giving verbal descriptions rather than simply giving them a map?

If it's because it's a secret (or, rather, the accuracy of the details is dependent on a skill check - if it were a secret you wouldn't be giving anything at all), consider why you're doing this. Is there a serious doubt about the ability of an experienced adventurer to accurately judge the size of a room they've walked into and the position of visible features within the room?

Is it because the accuracy of the map is dependent on the player's out-of-character skill to transcribe your verbal description to graph paper? Making things dependent on out-of-character skill is usually bad, and this is even worse: the characters can see the room; they're not going to walk into a wall because the mapper accidentally drew the door too far to the right.

Why do they need maps of every room at all? My group only uses maps when tactical positioning is important (i.e. usually during combat).

The fact that you're verbally communicating the information is itself a time sink. How long does it take to say "The room you just entered is 30 feet across, 40 feet long, the entrance you came in is 5 feet wide and 5 feet along the near wall, and there are other exits, positioned at 10 feet along the left wall, 20 feet along the right wall, and a 10-foot wide exit at the center of the far wall". Now how long does it take to draw a few lines on graph paper?

The only reason I can think of for giving a verbal description of each room and a list of exits is if you're trying to copy the feel of text-based adventure games, and if you really want to do that you should consider room description cards that they can read at leisure.

This isn't a great answer, but I don't have the rep to add a comment, and I feel like the idea could contribute to someone else creating a good solution . . .

Make a multi-layered physical map with a semi-opaque substance like wax paper? Do a detailed map, then loosely trace the outline of the detailed map on the successive layers of paper. The top layer would be completely opaque (you haven't entered the room) and you tear pages (or parts of pages) off as they explore. The second layer would be a very cursory drawing of the room, as in "this is what your party remembers as it was chased through the room by a rabid horde of three fluffy white bunny rabbits." After that have as many layers as you need, with the final being an actual measured map. If you have "hidden" items, you can also draw those in upon discovery, preventing the group from losing interest when the whole map is revealed.

Based on your clarification, that its taking 30-45 seconds to describe rooms to the player mapping them out, I have to state my first impression...

You are not the problem.

If your players can't stay focused for 30-45 seconds as you describe the room their characters are in... the rooms their characters might fight and even die in... that's their flaw. They need to put down the energy drinks and pixie sticks, and learn to focus on the game. Or at least show some common courtesy. If the only thing that keeps their attention is rolling attack dice, perhaps they should stick to computer gaming.

Now, I have been in games where the mapping became tedious and it took absurd amounts of time because the GM and the player doing the mapping were just going overboard with unnecessary detail. But that does not sound like your situation.

That said, a couple of suggestions...

• Develop a more efficient means of describing the room. One thing I switched to many years ago is to give the player doing the mapping drawing instructions, not a description of the shape of the room. For example... "from the south side of the doorway... go east 2, south 4, east 4, north 4, doorway, north 4 more, and square it off". Basically, you come up with a sort of short-hand between you and the player doing the mapping. I found that greatly speeds things up.

• The other thing I've done over the years is reduce the number of rooms in complexes. Gone are the 50+ room dungeons. Instead, 5-10 rooms are more typical. Basically, I trim out a lot of rooms not-essential to the plot. I also use a lot more outdoor encounters than I did when I was younger.

• If you are using someone else's map, perhaps you can draw out the rooms before hand on a small, cheap notepad. As they encounter the room, you hand it over to the mapper to add to his map while the other players down their next energy drink.

In almost every D&D game I played, the standard was "The Dwarf is mapping." Yup, an NPC, usually.

If not, we assumed the Character was mapping without having the Player go through the act.

It worked for us.

In general, if you want someone interested in something you have to give them a reason to be interested. If you can't engage your players in the mapping process, get the mapper to do it.

Maybe the mapper sees something he wants to investigate, based on prior player experience, but his character wouldn't care about. Him asking is essentially metagaming and an argument that another party member knows can be met with 'then he should've asked'. It sounds petty but if your party is motivated by loot (mine always seem to be) a lost chance at loot will gather everyone's attention.

(I think) You mention you're getting people together in person kind of infrequently, I'm not sure what your party is doing instead of caring about mapping, but if its catching up or something, you might be able to solve that with some socializing pre or post session. Sometimes my group is drinking instead of listening, so you could try to curtail that as well (we tend to set the stage and have a drinking party the first evening, pass out and then play in the days following that, your dynamic may be different.)