You say the owner's name was Neilson -- the colors you describe in the kilt could be the MacNeil tartan. Why not snap a picture next time you are there (if they allow photography) and post it. I bet I, or someone on the forum, might be able to ID it.

Or not... I was recently in the Charleston museum and saw two tartan items -- a child's kilt and a man's vest -- both in tartans never before identified. I was able to make a reasonable guess as to the thread counts and both tartans are now recorded with the Scottish Tartans Authority.