Any recent changes in wiring?
Any recent "smokage" in the wiring?
Here's how these work, the dash lights are a bit of a "trick"
The headlight switch has TWO power sources
1....Headlights ONLY power comes UNFUSED off the ammeter black wire direct to the switch which has a built in breaker. This SHOULD be unrelated
2...Tail, park, and dash light power comes from the tail light fuse. That power goes through the light switch and TO the dash dimmer control. Through the dimmer, and down TO the fuse panel on a tan wire. Through the INST fuse which is all the way to one end of the fuse panel.
Then out that fuse on ORANGE wiring to all dash dimmer controlled lamps
Unless something as melted and shorted, or recently been mis-wired, I don't know how this happened. You recently added a tach, etc? Changed the radio?
And, one last thing. Rotate the dash dimmer control, open and close the doors and see if that affects the problem. There's a wire on a contact, connected with the dash dimmer......this is grounded when you twist the knob left to turn on the dome lights. If this somehow got shorted into the dimmer control, that "might" do it.