Hello Mike! Welcome to irv2.com

You are correct that the vast majority of wiring issues are a poor ground. Buy a cheap 12V power tester, it looks like an ice-pick with a lead out the top. (about $3) Clip the lead/alligator clip to a good ground first, then puncture the wire with the ice-pick tip to find a live wire.
First, does the right brake light work? If it does, than means that bulb has a good ground, because the brake filament is also the turn signal. That would narrow it down to the right turn signal wire somewhere in the trailer wiring. You said the tow vehicle plug-end is working correctly because you've towed other trailers and the right signal worked-right? OK, that eliminates the tow vehicle, now you can concentrate on the trailer end of the problem.
In the trailer 12V wiring you should find a junction box or similar central point for the umbilical cord to connect with the trailer wiring that is hidden in walls, floor, etc. This is where you can access the right signal wire/right brake light. Test for 12V there, if you find 12V at that point you are slowly isolating the bad point. Continue to trace that wire for 12V as best you can. Hopefully you'll find the problem before you must begin tracing that wire behind walls, etc.
Oh, did I mention I too detest wiring problems.

Good Luck, let us know your results.