Hello , and Welcome to iRV2.
Sounds like you have a classic , bad ground , or 2. If you hooked to another trailer and everything worked, sounds like the truck is fine, then the lights on the trailer aren't properly grounded to the trailer frame. Pull the light lenses off and look for corroded mounting screws. Most of the trailer lenses aren't water proof and are prone to this kind of problem. Pull any screw in the light that touches metel, the ones through plastic aren't an issue, clean the screw, and the metel sorrounding the screw hole ; steel wool or sand paper; and try the lights again. Also check the main ground wire from the plug where it hooks to the trailer frame.