Broken wire, bad ground, corroded socket. I'd see if it has power to the socket first. If so, probably bad ground. Those have plastic housings IIRC, so, a separate ground wire. Use a temporary jumper wire to use as a ground to verify that it's the problem. Find a good ground, like the trunk latch for one end, and the actual socket for the other and see if it now lights up. It might be easier if you have a helper to either press the brake pedal or hold and view the wiring/lights.