Bad earth connection at light cluster?
How about a malfunctioning brake light switch
A bad ground wire is the most common cause of turn signals and brake lights not working. The ground wire connection might be corroded.
the blinker switch shorted out the brake lights... really really common problem, need to replace the switch
The next thing to check is the switch that activates the brake lights. It is probably on the master cylinder.
The tail lights are on a separate wiring than the blinker/brake lights. Look for a blown fuse or a broken/loose wire.
The GMC dash tail and parking lights are on a different fuse from the brake lights. Check the fuses for a possible blown fuse.
try replacing the flasher. there should be two, one for flashers and one for turn signals
probably your blinker switch (multi-accessory switch). The high mount brake light is wired directly from the switch on the pedal but the rear two lights are wired through the pedal switch and then through the the blinker switch on the steering column. Almost all of those blinker switches go bad.
Check the brake light bulbs, Check the brake light fuse, Check the brake light switch, In that order.
Problem most likely is in the Turn Signal switch. I had same problem , replaced Turn Signal switch assembly and that fixed it.
Check the park lamp relay. It is probably next to the fuse.
whats the color circuit for the blinkers an break lights?