Ok I have a 89 Chevy K1500 that has a weird electrical issue. When I start the vehicle in the morning I turn the headlights on with the switch and they come on instantly but the tail lights and dash lights sometimes take a couple minutes to come on. I have noticed that the colder it is the longer it takes for the dash/tail lights to come on. The headlight switch has been replaced but I haven't noticed this issue until the winter when a cop pulled me over with no taillights. I can some times turn the light dimmer wheel up and down on the headlight switch to get them to turn on faster but it's never when I turn the headlights on.
Sure sounds like a headlight switch issue to me. I'd check and make sure the wiring isn't melted or burnt behind the switch, too.