GMC troubleshooting questions? Ask a mechanic for answers
This is typical of a poor ground to the lighting circuit. Just where the ground has failed is something you're going to have to work on, but when a ground circuit fails, the electricity will often find an alternative path, which is through another light bulb, and this causes that bulb to glow as the power is running through it.
I would start at the rear lights themselves. Run a redundant ground to the circuit and see if the condition suddenly goes away. If so, you'll know you need to correct the ground circuit issue.
You mentioned that the brake lights flash when the signals flash. That was my clue that you have a ground issue. You still need to find out where the faulty ground is, probably where it attaches to frame near the rear bumper underneath, but if you run a redundant ground to that circuit using a jumper wire, that will prove the theory and you'll know you're on the right track.