It would be helpful to have a wiring diagram. Does your trailer have a circuit for the brake lights that is separate from the turn signals? I have also seen a poor ground connection cause strange symptoms like that. The ground wire on the trailer side is typically white. That connects to the black wire on my isolator block/relay. I would not rely on the hitch itself to provide a sufficient ground.
37 panel, Well Sir, not sure just exactly what your problem is. At the risk of maybe sounding dumb, but, your bike is a "5" wire system and maybe your trailer's a "4" wire??? Make sure you haven't crossed any of the brake light wires with the turn signal wires on both the trailer plug on the bike and, the trailer plug on the trailer.
If you unhook the trailer plug from the bike to the trailer and then test all the lights on the bike, do they all work correctly? If so, then test the trailer plug on the bike with a 12V test light and see if you're getting all the correct signals as you have a friend activate all the different functions, i.e. rt turn, Lf turn, brake, running lights etc. If all that's good, well, I'd say you've got a problem in the trailer wiring. Let us know what you find Sir. Scott
P.S. Sorry Ron, didn't see you're answer before I was done with mine. Scott