Check out my post from 8/2, just above yours. Most problems related to the dash dummy light rear-light problem annunciation are due to a grounding problem with the taillight assembly ground plane, as documented in great detail elsewhere on this site. I've gathered that this problem is more common, if not uniquely common, on newer-than-01 models, and it was eventually addressed by a BMW recall.
My problem, also an 01, (and with same dummy-light symptom) turned out to be a completely different issue -- damaged / broken wires within the wire bundle that is located inside the rubber boot that leads from the trunk lid to the body (on my car, attached to passenger-side hinge strut). My license plate bulbs continued to burn out, apparently due to their constant flickering on/off due to the shorting wire lead located within this rubber boot. The lead to the license plate was all but broken in two, and several other wires also showed considerable insulation damaged with some exposed wires . It almost looked as if the insulation was cut, as if the wires were damaged before or during installation, and not by opening and closing of the trunk. Of course, there is no way to say for certain.
To check this out, carefully slit the boot open on one side with a sharp knife to expose the bundle of wires therein, and take a look. Repair any damaged wire(s) therein as/if necessary, and then tape boot back up with electrical tape, and reattach it to hinge strut with strip-ties.
Last edited by waterdale; 09-28-2012 at 09:28 AM.