Jeremy,
Check to see if there is 12v to the relay trigger by putting a volt meter across the wires to pins 85 and 86. If you see 12v the relay is being told to close so your problem is before the relay, maybe brake switch itself. If no 12v there, check pin 87. If 12v there, problem is between relay and brake lights. Based on what you said, I suspect problem is between brake switch and relay, but check to be sure.
Steve