There are no fuses in the trailer for lights, those fuses are in the tow vehicle. Surely sounds like a wiring issue in the trailer though. The running lights are a single wire on the trailer 7-pin. So if one side is working and the other isn't the problem would be with the trailer wiring or a burnt bulb, but I expect you checked that already. The Brake and Signal light share a wire for each of the right and left side, so that is worth checking at the plug.
2011 Jayco X19H (purchased 2015)
2008 Jayco 1007 PUP (purchased new, traded for the X19)
2018 Nissan Titan Midnight Ed.