i towed a trailer behind my 85K100RS for several years, never had an issue or tow-related problem. reynolds made/makes hitches for K's, you can often find one for sale on e-bay, craigs list, K-forums, etc.
i made my trailer from bits/pieces of other trailers, it was 4' x 4' utility type, used to haul whitewater kayak and camping gear all over mountains and roads of TN, NC and WV. I would purposely reduce speed on twisties while towing just to be safe other than that i made no compensation for towing and seldom knew trailer was there.
I don't know if it's standard on commercial trailers but i built my hitch so that is would rotate as bike leaned over in curves.
sadly, no pictures.
g'luck