I got back recently from traveling around Korea. I did find a few keyboard shops, so I'll share the info for anyone who reads this in the future.
The two I tracked down in Seoul were Leaderskey and Funkeys. There was some info online about these from a few years back, and I'm happy to report they're both still in business. Leaderskey was my favorite and I purchased several items there.
Leaderskey is a Leopold / Filco / Realforce shop, so predominantly Japanese and Taiwanese factory-assembled brands. It has a showroom with lots of products available to test out. You can order on the spot and they'll get your item out of the storeroom.
Leaderskey is very easy to access, and as of this writing is open Mon-Fri 10:30-18:50. It's practically inside the Sinyongsan metro station, which is immediately east of the Yongsan mainline rail station. Yongsan is the station just south of Seoul Station, so this is very central. If you go to exit 5/6 of the Sinyongsan metro station, exit 5 is off to the left and exit 6 to the right, and there's an underground shopping center straight through (i.e. remain at the basement, metro concourse level). Leaderskey is inside this shopping center on the left side, and you'll walk past their stockroom filled with racks of keyboards to reach the shop itself. Their website
http://www.leaderskey.com shows everything they sell and whether it's in stock. The site is entirely in Korean but Chrome auto-translate does a decent job on it. If like me you are specifically after some Leopold hardware then this is the place.
Funkeys is in the same general area. It's a bit out of the way, but still not hard to reach. Note that it is no longer on the fifth floor as indicated in some posts you may find from a few years ago: they have moved up to the 13th floor of the same building. As of this writing, open Mon-Fri 10:00-17:00.
Funkeys seems to specialize in mainland Chinese prebuilt brands like Varmilo and Ducky as well as kits, switches, etc. for custom builds. They have a nice showroom, but they seem to mainly function as a webshop and their showroom does not really reflect what they stock. It was full of nice all-metal 65% Varmilo boards, which they informed me were prototypes that never went into production and are not available for sale. They didn't seem too receptive to my interest in buying the display model. Nonetheless I got to test out Varmilo boards for the first time there and learned a thing or two about boutique MX clone switches.
Google maps seems to have an accurate location and business info for Funkeys:
https://goo.gl/maps/5tWuTFqvJ4V9p3VL8However Google Maps is generally not very useful in Korea and I had much better luck with Kakao Map overall.
Some older guides describe walking to Funkeys from Sinyongsan, which makes sense as many people would group this with the nearby electronics market. But I found it more straightforward to reach the shop by walking south from Hyochang Park metro station instead of northwest from Sinyongsan station. It's on the 15th floor of the Hana Building, with a nice view of Seoul from their showroom.
Note that in both places little or no English may be spoken. The staff are very helpful and welcoming, they just won't be able to help you out much if confronted with a foreign language. So practice your Korean greetings and thanks, pick out items you're interested in on the site first, bookmark some pages, and pre-translate any questions and requests, which will avoid putting them (and you) in an awkward spot.
And note that both places are closed on weekends! Weekday hours only.
