I had the same problem with my 2002 Jetta, and I'd put money on it it's the same fix, especially with your comment about the reverse lights failing. If you open your trunk, you can see a wrapped bundle of wires that is clipped to the left trunk hinge mechanism. There's a point where this bundle kinks a bit, and over time the smaller wires inside become brittle and crack. When the various cracked wires touch each other it causes shorts. I fixed it myself using a fantastic online howto for this exact issue, which I unfortunately cannot find right now.
Oh, and the wires that run through this bundle run the reverse lights, the license plate light and the trunk latch/sensor. (Maybe more but that's what I know of.) So could cause problems with various combinations thereof.
(Came back and edited my answer because I found the link: http://forums.vwvortex.com/zeropost?cmd=tshow&id=3804453)