'04 Brake light is dim on passenger side

Check for high resistance at the connection points, particularly the ground.

 

I have exactly the same problem with the same brake light. The connections to the light are tight, and nothing done with them seems to effect the problem at all. Without stripping the interior I can't find where the wires lead, but they appear to come directly out of the harness.

Has anyone else had this problem? What's the solution?

 

I would use a voltmeter and measure what was happening. It should be possible to connect to the wires in question without damage by use of small pins through the insulation. Slide them in at an angle to the wire, rather than perpendicular. Have a helper press the pedal and see how much drop there is. If there is little drop, i.e. the voltage reads close to 12V, then it is the LED. If there is significant drop, then there is a resistance in the current path somewhere. My schematic says the switched wire is blue, and the ground connection is white-black, but yours may be different. The ground point for the lights is BN, under the rear hatch in the middle.