I don't think it has something to do with the skin folders name, that should be OK.
I tried in BAT and had the same result, when selected no skin showed up.
A look into the log showed this:
[2019-10-24 14:21:30.056] dT: 0 INTERNAL ERROR: '3DO/Plane/F84F/summer/skin1o.tgb' Invalid image type (need in 32bit RGBA).
[2019-10-24 14:21:30.056] dT: 0 INTERNAL ERROR: TGA '3DO/Plane/F84F/summer/skin1o.tgb' has unsupported format
[2019-10-24 14:21:32.493] dT: 0 INTERNAL ERROR: '3DO/Plane/F84F/summer/skin1o.tgb' Invalid image type (need in 32bit RGBA).
[2019-10-24 14:21:32.493] dT: 0 INTERNAL ERROR: TGA '3DO/Plane/F84F/summer/skin1o.tgb' has unsupported format
btw: a log ALWAYS is helpful.
When I looked into this F84 pack it turned out that the defSkin TGB file of the F84F has a size of 16MB
with a size of 2048x2048 and/or too many colors (?). Sadly I forgot (wasn't into this kind of stuff
for years now) how to handle this and make it a working 4MB TGB file.
So I tried another "quick" fix for my BAT Install with just making a folder FG84F-Fix with subfolders
3do, plane, F84F, summer and put there just the files from another F84G summer folder
including the 4MB TGB file, but sadly that that didn't work as those F84G defSkins aren't compatible
with this (new) F84F swept wings Paint scheme (the old F84Fs were afair)..
So when I tried this dirty fix a skin inside the F84F paintschemes skin folder was shown then
when i selected it but as explained above: its unuseable.
Seems what we need is someone who knows how to make that F84F 16MB TGB file a working one
and post it here, then we can try again to solve this.