Travel Trailer running light not working correctly

A very useful check is to take the lens cover off both light sets and look carefully at both. The thin filament is the run light, the thick filament is the brake/turn.

Check the operation of both to see that they work the proper filament, change the bulb with the other side to see if that changes anything, and take a wire from the negative of the truck battery, to the side of the bulb at the back to check the grounding of the bulb. If you find anything with one of these, come back again.