Verify the voltage at the end connector pin pulses with the turn signal on, with no trailer connected.
If it does the circuit is ok and there is a shunt to ground on any other trailer you connect.
Maybe the trailers are wired in error for some other towing vehichle that is also wired incorrectly with a ground on that pin in the wrong place.
This is why there are color code and pin number standards so any trailer can be plugged in without issues.
If you can't find the issue now, I'm out of ways to help.
Good luck.