[sierra77]

I had the same problem with my '96 LS when I bought it three years ago. Mine would flicker every so often, so I knew that it was something other than the fuse. I figured out that it was the actual headlight/dimmer switch. My buddy works for a Chevy dealership and told me that even with his price, the switch is over $80. I decided not to go that route since mine was a work car, and I didn't want to put that amount of money into little things like that.
I studied the wiring diagram in the back of my Haynes manual and bypassed the dimmer portion of that switch. So now my dash lights all work, but are all on the full brightness. I don't mind since I never dim my dash lights anyways. The switch still works in the all the way up position to turn on the dome however. If you are not up for the task, I'd try a new switch.