The reverse light is most likely a reverse switch gone bad. Happened in my focus. It's a cheap part, I forgot how much the fix cost. Don't know about the cigar lighter, a fuse would definitely make the most sense.
Heres a how to on the reverse switch.
Originally Posted by Deftmetal
the red door is required by some race rules to identify the driver
ROTM June '13, PNW Crew #42, SR #245, Rally Rev #02