Sorry, yes, that's heatshrink, I don't use crappy electrical tape in my upgrades. 
I spliced in the extra wires to go to the regulator module as the wires that were there go to the connectors to join the two pickups. Other than the extra wire for the jumper between the two with the connectors, I didn't need any extra wire for the job, just used what was already in there.
I ran into an interesting issue with the dome car, the windows are wrap-around so you could see the side of the LED strip, I didn't like that look. However, in looking at the spare parts, the obvious solution presented itself. I just stripped everything out of one of the old bulb holders and cut away all the middle supports. I screwed that back in, and it neatly covers the sides and still lets the LED's illuminate the interior of the car.
