Is this a problem with the lights on the vehicle or the trailer? Do you have access to a voltmeter?
Being the third brake light is working really proves that most of this ciruct is working. I would advise you to check fuse #34 VEH STOP located in the rear fuse block. This is the only fuse after the brake light switch. I would verify that the fuse is not blown and that the fuse is getting voltage when the brake lights are applied. Here is a wiring schematic of this system so that you can better see how it is wired.
Feel free to contact me with any questions! Good luck!
Is there voltage to the wires? There have been some problems with the light bulb plates. Actually gm recalled some of these. I am primarily Chevy, but if you post your vin# XXXXX can see if this applies to your particular vehicle. Actually if you look at the number on the tail light board, we can tell if your vehicle has had the updated boards.
GMC -- New P/N 16532716
Ok well there seems to be some thing wrong with your vin#. I cannot check to see if any work has been preformed or if this works needs to be done. If you count back 8 digits from the end of the vin#, you should have a 3 meaning your vehicle is a 2003. The part number you have listed is not the updated version. So if the board is not correct and the vin # XXXXX in the following catagory you should have your local dealer replace these for free! Here is the vin breakpoints that you must fall within. If you get me the correct vin# XXXXX can be certain of if you qualify. These numbers are the last 8 digits of the vin#. Your needs to fall inbetween to be accepted.