It definitely sound like a wiring problem.
There's a main connection to all of the wiring that goes to the rear of the truck behind the LF wheel well fender liner at the bottom rear right next to the cab mount.

The fuel pump wiring is also in that wiring bundle, so if you disconnect it the truck won't start (along with all the rear lighting, trailer included won't work).

If the trailer light issue is some that started with the trailer all along, I would also check to verify that the trailer plug is wired correctly, since there's a positive power lead wire in the plug on the truck.