If your third brake light is working, I would imagine that the relay isn't bad. When you press the brake pedal, do you hear a relay kind of click??
If you do, then it should be ok. Follow the wires as far as you can coming from your taillights, and make sure none of them are cut or grounding out on something.
If you do, then it should be ok. Follow the wires as far as you can coming from your taillights, and make sure none of them are cut or grounding out on something.