Some tail/turn light assemblies have 3 wires; turn, tail, and ground. Some only have 2 wires, tail and turn, and use the metal frame assy as ground. And the metal frame of the light assembly is bolted to some part of the metal frame of the trailer since the trailer frame is ground back to the battery.
If you have three wires, then determine which wire is the ground wire and trace it to where it attaches to the trailer frame. If only two wires, then make sure the light assy frame is clean and well connected to the trailer frame.
I would also check the ground wire coming from your cord plug to make sure that wire has a good connection to the trailer frame.