Holy sh*t, I wanna do the same thing but thought I'd leave it until I knew enough about about the wiring and that.
Guessing the details will be in the mighty Haynes manual... Which should be duly arriving on the 25th - otherwise Rudolf gets a cap in his ass.
This is just a guess (as im still looking to whether i wanna do it) so if im completely wrong then im sorry!.
Naturally you'll need to locate the the wires that goes to your interior light. I suppose they get wired into the fuse box or something.
Buzz the wires out with a voltmeter as I think neons, like LED's, are electrolytic sensitive. One should be 12V (you'll have to have the door open too) and 0V (GND) i think.
Then cut the cigerette lighter adaptor off your neon wiring. If the neon is indeed sensitive to the polarity then i suggest to grab your voltmeter and set it measure resistance.
Make sure you know which probe is grounded/earthed
Test both ends and see if you get either a MASSIVE resistance or a relatively low resistance. Low resistance is what your after, make a note of which wire is touching the 'Ground' probe. You need to connect that to the 0V wire and the 12V to the other.
As i say i may be way off the mark on this one but i'm sure someone will know something. Soz if its confusing
Let me know if you have any luck.