One more thing. On most GM truck, burbs etc. there is a seperate fuse panel under the hood for trailer light. Back up lights could be working on the tow unit and not on the trailer due to blown trailer fuse
Now to get you really messed up Yellow is Left bright, turn/brake, Green is Right bright, brown are light and marker lights with White as the ground the world around.
Over 1/2 the trailer lighting problem come from bad ground. There are two green wires in the the GM truck wiring the Dark Green is the right bright. The LIGHT Green is the back up light. Don't cross em up. To check the trailer you can plug the brake plug Male) in the the brown (Female) and turn your lights on and if brakes let you back it's in the tow unit. Confuse yet??
I have fixed a many a 12 wiring problem in and most are ground or blown fuse. Check the wiring in fold away trailer the rub and cause a short. Good Luck