One brake light stuck on, the rest not working?

I would start at the rear lighting junction box. It's under the truck mounted to the rear frame crossmember (thanks GM) They are very bad for corroding internally and causing lighting problems. Are the front lights working? Headlights?
First look at the block and unplug C1. See if the light goes out. Now use a cheap incandescent test light to test for power at the connector not an LED type.

https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester

In connector one with the key on and the lights on there should be power on pins D&G those are the markers. Now check for power on pins A, B and H Then have someone step on the brakes and test again Write down all the results. Turn on the left and right turn signals and write those down. You should see the light flash on pins A and H and when the brakes are on there should be power on pin B. If that all checks out the fault is in the wiring block/trailer box. Replace it. The screws holding it will likely fail, I just grind them flush and mount the replacement with new nut and bolt combos.