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I checked with a meter and found that the brown wire from the switch to the rear block connector is good. Also checked the switch with the meter and found that the switch is good. Ckecked the brown wire fron the rear block connector to the tail lights and found that their is no continuity in that wire. I found corrision in the driver's side inboard tailight. I cleaned it all up and replaced the bulb. I also did the license plate light and found that it was in good shape with no corrision and I replaced the bulb. I am in the process of doing the rest of the lights now to make sure that they all have good connections and bulbs. The two that I have done did not fix the problem. Will report back back when I am done.
Here is what I have done to the rear of the car. I have cleaned all of the tail light and license plate sockets of any corrosion and replaced all of the bulbs. I have found where the brown wires along with a black ground come out of the harness at the license plate. I have not found where the brown wires all connect. Are they soldered together or just twisted together? Do I have to unwrap part of the harness at the license plate to see the connection? I am making progress but still have not found the problem. All brake lights and turn signals work correctly as well as the backup lights.
If you're sure you have it at the brown wire coming out of the connector, the problem is between the two red arrows. It's a straight piece of wire from front to rear.