Just to say this post was really useful for repairing my third brake light. After disassembing the rear spoiler, I used the multimeter on the LEDs and they showed low resistance (or is it resistivity? Electrics are not my forte), so I checked the wires coming out of the back. Lo and behold, they were only churning out something like 4 volts so I inspected it closer, and after removing some tape it became obvious that some cowboy had done a crap job repairing what I can only surmise was a broken wire. I managed to solder a new wire in place and the brake light works like a dream. I also had to fix the washer fluid tube on the other side that was broken in 2 places, which also seems to be a common problem.
Either way, thanks to everyone in this post for all this info.
C5 III Tourer 2010 3rd brake light
Moderator: RichardW