When I turn switch to headlights, all lights go off including dash lights.

It could be the switch. However it sounds like a bad ground somewhere. Grounds are tough to chase as a ground for something else that is in the engine bay could be bad and back feeding into the dash.
To test switch, remove and check for continuity in the on position with multi-meter.

my '92 had a slightly similar problem that went away. I drive with the lights of, and at night the dash lights start dark and gradually come on over a minute or two. Obviously an ambient light sensor somewhere...

If it goes away that is okay but there has to be something wrong that will more than likely return and it is a safety issue where you might not even notice your llgihts are out.