My dash and radio lights go out when I turn on my headlights.

first turn off you dome with the light switch. then have you light switch checked to see if it bad.its a start to your problem. then your light relay has to be checked.
along with your fuses and possible wiring problem.

You have a short (crossing wires) to the radio....is the radio factory or after market?

Probably bad ground in the dash circuitry. You'll have to pull it out and check all the connections. Big job.

change your signal light switch. i just had the same problem. cost me a 150.00 for an after market switch, comes with a full harness that plugs in under the dash.

Chevy caprice classic circuitbreaker

automatic headlights are controlled by a photo sensor on the dash located in front of the Instrument cluster. to test the sensor try covering it and see if the headlights come on. faulty wiring in the circuit could also cause this problem. the headlights and the radio are wired together and the "auto" function will cause the radio to get brighter when its dark out, thus the combination of problems.

have the output of the alternator check... and perhaps the battery posts may need cleaning as well.

Robert

The main switch is bad that turns on all of the lights. New a new switch.

This is not a voltage problem. The problem is in the headlight/dash dimmer. You have to turn the dimmer switch on the headlight switch to select what intensity you have right? try turning it down just a smidge and if it stays steady then it is most likely a dimmer switch problem. This requires replacement of the headlight/dimmer switch to fix. local auto parts shop should be able to have this in stock.
ps dont forget to rate my solution please. Thanks

Turn on your headlights and check to see if your taillights are working. They act as a fuse to your dashlights, its a safety thing