I"m back to thinking the problem is in the trailer itself. Check the ground, ground, ground. Okay, just where do I check that?
I'm certainly no expert, but what I know comes from experience. I had a nightmare of a problem with my '73 trailer. I have this light
with a pointy end and a clamp for the ground. Attach that to the ground wire from the hitch (with vehicle hooked up) and just start testing wires, assuming you have easy access. I did this to make sure all of the hot wires were indeed hot. When that tested out fine, then I knew it was the ground, so I just went through inch by inch (I'm not kidding!) through all of the grounds and found the problems: one splice was not attached, the previous owner/manufacturer had combined the grounds from the trailer's power battery
and the hitch. After some new connectors and wires, it works perfectly now. Most likely it's something simple, but sometimes we go through a lot to see just how simple life is--or in this case, trailer wiring. Good luck!