Ok, I wasn't sure what was going on with this dropout arrangement either.
My first guess was a disc brake mount or some sort of mount to attach a trailer. Is it my imagination that there was some sort of trailer made by the Taylors at one time? They sure made all kinds of stuff...kid's bikes, mixtes, stems, racks, etc. I'd have to agree with the previous posters that this set up was to mount some old style derailleur, though.
Jim Cole
Memphis, TN