Response:
It's either a bad ground or a bad light socket itself and very common to fail. Your wire harness runs down the drivers side just inside the frame rail to just below the left tail light where it forks and part goes up the other over to the right tail light with quick connectors for the license plate light. UNLESS, someone has installed an aftermarket trailer wiring package. Also check your trailer connection. even though your not using the connection you are still receiving power to the plug. use a test light to make sure it's working properly.
good luck
