This isn't going to be easy to fix, or diagnose through a text discussion, and I don't have a scanner to show you pics. If you have an electrical tester, and are familiar with terms like continuity and resistance- then I can probably guide you through some testing procedures- IF this is even a wiring problem. It could be as simple as a corroded connector, or as difficult to find as a pinched wire.
First thing is to see what works and what doesn't. If the parking lights don't work, then it's a lost ground. If the parking lights work, then it's a lost hot. You can verify that it's a lost ground by unplugging a light and testing the terminals for continuity to ground (ohms 0-.1). If you can't find continuity, then it's time to start tracing the wiring harness, and being a wire detective. Find where the harness from the 3rd light ties into the main harness- somewhere near there the grounds tie together and that's where the problem is.
The Helms manual says that if the 3rd brake light is operative, but the two other lights are not operative, then you should start by checking the GEM which stands for Generic Electronic Module. This handles all the switching and power controls for things like brakes lights, PW, PDL, Wipers, etc. The GEM is located behind the glove compartment, and you'll have to remove the glove in order to see it. Sadly, it's not one of those things that someone without the proper electronic equipment can replace. Well, you can, but things might not work correctly. There is a program in the device that must be downloaded before removing, and uploaded in order for a new one to work. Now you might be able to get one from a junkyard to work if you find a car with all the same accessories. You can check the connectors and pins for corrosion- but it's unlikely unless you've been spraying a hose inside the car or driving around with the windshield out in the rain. It's worth looking at if you can't find a problem somewhere else- but if you think you need to replace this and can't find one in a junkyard or don't want to: take it to a dealer.
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Originally Posted by the user formerly known as ZX3_Chick
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