2003 Chevy Silverado break light

My back left break light will not light up. the bulb is new and lights up with the all the other lights (running and night time) when turned on. I am not sure how long this has taken place, the truck did pass inspection last year. I had a cap put on and they spliced into the black wire and the baby blue wire..... that cap break light also works. I know that there are three wires that enter the socket for that light, black, baby blue and brown. I don't know if maybe inside the socket there is a short with the wire for the break because it lights up with the headlamps but not when the breaks are applied. thanks, Frank