Do you have an actual ground to the frame of the trailer? Many of the trailer harnesses do not have an actual ground to the frame. On almost all of my trailers i have had to take the white wire on the trailer side, add an electrical connector and screw it into the frame. Never a single light problem after this is done.
Yessir, there are a couple built into the lights that when the screw is run through it makes the ground connection. These are the only grounds.
Update: Still having the same issue, the 2 fuses replaced did not fix the issue. I have tested everything from the light to the tongue. Everything at the truck is functioning. I am completely confused. May start completely over and see if I missed something.