posted 07-16-2008 02:45 AM ET (US)
I just ran in to the same problem recently. Trailer 1 had torsion axles with the lights mounted on the fenders that were attached to the torsion arm. therefore isolated from the trailer's frame. Trailer 2 had leaf springs and the lights were attached to the trailer frame.
The problem did not show up on trailer 2 but did on trailer 1.
I found it to be the ground wire in the cars 4-pin wiring harness. It seems that trailer 2 got it's ground from the hitch ball connection. If you mounted new lights and attached them to plastic fenders you may need to run a ground from the lights to the trailer frame.