I know these trucks pretty well, and do alot of wiring/mobile electronics installs. It sounds like it is pulling a ground thru the domelight wire. This would tell me there is a bad ground on the light switch, or possibly a melted switch internally (very common on these trucks). The domelight has constant (12v+) & is turned on by the plunger being grounded (-) when the plunger is out. The plunger in the side of the dash has a constant ground and the ground goes thru the headlight switch on it’s way to the domelight. If there is a poor ground on maybe the headlights (on the core support), or the switch (behind the IP) the switch will try to pull the ground thru the path of least resistance (dome circuit).
There are also fuseible links in the engine compartment that can be “open” and not supply power to the proper wires in the truck. These are fairly easy to test if they are good or not, with a continuity tester.
Again, this would be easier to diagnose in person than over the interweb.