Right side brake light not working?

If none of the lights on that side work, then I would check the ground wire for the lamp assembly on that side. It is the black wire. If it is only the brake light that is out, then you need to use a test light to check for power for the brake lamps which is the white wire going into the lamp housing. GM has had bad connectors and bad lamp housings multiple times so it could also be a bad housing. Testing should show where the issue is. The attached wiring diagram shows the wiring that is shared between all of the tail lights as the brown with white wire, which connects to three different marker lamps on different colors at the lamp. Then the White wire for brakes which is shared with both sides and the Dark blue with white for the right turn. Use a test light connected to ground to test for power at the connector side.

Okay, that would be the white wire for the brake light, you can disregard the ground and other wires and just test the white one. If you want to make it easier, pull the light out and jump power to the white wire using a needle pushed into the wire. Just apply a small dot of nail polish or liquid tape to seal the puncture. You can also test the same way, connect the test light to ground and touch the needle with the brake pedal down.