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If you have voltage on the brown wire behind the taillight, and the bulb is good and the socket is good, then there is really nothing else it could be.
The ground must be good, or the other lights would not work when you turned the headlights on, or the parking light would only work with the brake light off.
did you make sure both of the wires inside of the light bulb light up....there should be two....one for the bright lights (brake,turn, flasher) and one for the dimmer lights (parking, tailights), one of them can break and the other one will still work just fine. I would put a new bulb in before i went any farther (unless you already have and i just misunderstood)
Yes I tried a new bulb but I only had the parking lights on not the headlights will this make a diference and I tested the wire in question with a test light and you said two wires but I only have three wires in going to the socket. I assume one is ground one is for brake and turn and the other is blue with a orange strip it is the one I have no juice on with the test light. The left side has juice on each wire when I put the test light to them. And just so I know we are on the same page this is rear lights not front parking lights.