My Ford had a 1-wire dome light, the ground was through the bulb base to the a tab where the light mounted to the roof. My harness kit was a black and white wire... carumba... I found a 2-wire socket at a parts store. I made up a new mounting tab, attached it with JB Weld. I had to run white wires up through my a-pillars and a black wire across the bottom inside lip of my dash. So start with seeing what you have for a light socket, 1 or 2 wire and see what the harness instructions show. Compare that to the car schematic if you have one.
Open the doors one at a time and manually push in on the switch plungers and see if the dome light goes out. One or both of the switches may be defective or not getting enough travel on the plunger to open the curcuit when the doors are closed.