Have you checked to see if you have voltage on the brown wire? Measure it with the lights on but no brake. Use a test light or a meter. It's either that or a bad ground to the socket. Socket wire crimp joints go bad in time. Problem could be there.
Yeah, it's probably just a bad connection. if one of the lights is on, and the other one isn't, you obviously have voltage to the rear. I'd do as John said and check the voltage out of the connector, and see if you have a loose connection either at the connector, or at the splice. Check the ribbon cable that runs along the drivers side as well, you can get to the connection by taking off the small panel in the rear of the bed. The main connection from the ribbon cable to the rear light harness is right there.
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