Grounds are ALWAYS a huge issue with trailers.
If the wiring harness is grounded through the trailer plug, try removing that and seeing if the problem disappears. (ground the trailer wiring harness to the frame of the trailer in other words)
As simple as trailer wiring is, you'd think it would be foolproof. In actuality, I'd be willing to bet more people have problems with 4 to 7 wire trailer harnesses than people have problems with the entire stock truck wiring harness.