1991 corolla no dash lights when you turn on headlights the radio & heater won't work

Have you tried to replace the headlight switch? I ask that because you say the radio and clock go out, with the headlights on clock and radio go dim, so not so bright at night but bright in day to see them. So maybe the switch is bad?

have you checked the headlight switch itself could be a faulty light switch

a short or a fuse

With headlights on, try to start the car.
While engaging the starter: Do the lights dim? Do you hear anything? If so, what do you hear?

you dont know where the dimmer is? on the left, on the headlamp switch or a small knob.

PROBLEM COULD BE A FAULTY TURN SIGNAL COMBINATION SWITCH.

It has something to do with the climate control. You have to have a technician repair it. ebay has many of those repair guys for mad cheap. I did my L of of ebay. They have ways of removing dash and climate control off of google. Just engine search it. Look for people that fix Dash and Climate control. If that does not work then it is a LD problem and probably need a new Radio.

You likely blew a fuse for your lights. Here is a wiring diagram for the original radio.

This is a problem with all trucks what you need to do is get the dash or cluster out and get it repaired at gm they send it out and after a few days it will be returned functional

bad ground on battery to engine block,use jumper cable from negative to a metal bracket on engine and see if that resolves issue if so get a new ground cable.