Typically trailer light problems can be traced to a ground issue. You didn't mention if it was a 4-wire or 6 setup, but regardless there is a ground wire on both sides (vehicle and trailer). I'd start by checking the ground wire where it terminates on the trailer and make sure it isn't broken or corroded.
You can also try running a separate wire from a good trailer grounding point (no paint or corrosion - metal only) to a like point on the tow vehicle and see if that doesn't lighten things up

EDIT: Here's a good site that might help you out:
etrailer.com | Trailer Wiring Diagrams