Have you checked your bulbs ? The tail light / brake light bulb has 2 wires inside it In my case I have had to change each bulb because the brake light portion did not work but the tail light portion of the bulb did ( I'm assuming that your front park lights are working )
Wrong bulb
Fuse
Are you saying your tail lights themselves do not work and only the brake lights work. If that is the case, check the fuse, and then check the tail light bulbs.
Probably a blown fuse.
Look for a fuse labeled TAIL LIGHTS. There are 2 separate circuits, one for brake turn and flasher and the other is for tail lights.
Tail lights are usually on the same fuse with interior lights and dash lights. That is so you will know when the fuse is blown. Brake lights are usually on a different circuit. If a fuse is blown, try to figure out the cause rather than just replacing the fuse.
The tail lights and the stop lights work off of different circuits. The stop lights work when the brake pedal is depressed while the tail lights work when the light switch is turned on. Look for a burnt fuse or a bad connection.
The tail lights are on a separate wiring than the blinker/brake lights. Look for a blown fuse or a broken/loose wire.
Most likely a fuse.
Fuse, wiring, bulbs
if the tail lights work but not brake lights then its most likely just a blown fuse or it could be the switch at the top of your brake pedal arm.
The GMC dash tail and parking lights are on a different fuse from the brake lights. Check the fuses for a possible blown fuse.
Simple your tail light bulbs have fused and needs replacing