It's on the same circuit as the parking/dash lights so if those are working, it isn't a fuse or relay.
I suspect that you have a short somewhere in the harness and if it is all door switches, then it's gotta be upstream of the branch in the harness where circuits go right and left to either side of the body.
If you have a volt meter you can check continuity between the switches and where the harness emerges from the body back into the engine compartment.
Definitely. I believe the lights in those switches have their own power connection to the headlamp switch. If you can check the power on that circuit back to the switch, you might find a ground problem.