sounds like either your tailight harness or your trailer is wired backwards. if the trailer works correctly on other vehicles, you need to flip the R/L wires on the tj to make it work with your trailer. R/L is a wiring issue, not ground issue. dim lights=poor ground, weak signal
make sure the ground wire on the tj side and the trailer side are good/clean/tight. also, make sure theres not alot of surface rust/grease on your trailer ball and cupler. the ground on the harness is usually in most cases is just a secondary and the trailer is actually primarily grounded through the ball to the vehicle. the white wire supplies a constant ground so that your lights dont flash when you hit a bump and the coupler rattles, or if your ball doesnt make good connection.
on a 4 way flat harness:
yellow-left side blinker/brake
green-right side blinker/brake
hope this helps. if you need more info just ask.