Take it to an auto electrician, they will test and diagnose the source.
check the fuses - there is no fuse for the headlights.
Check bulbs & fuses first. If still a problem you will need to start looking at possible wiring issues
check the fuses
If the headlights are not working correctly on a 1990 Corvette, the fuses or lights could be going out. Replace the old fuses and check that all wires connected to the lights are functioning correctly.
Have you checked the fuses?
check for blown fuses
Check the fuses and the bulbs.
Check fuses, common circuit
Check your fuses.
Check the fuses. If they are good then you will have to replace the headlight switch.
Check your fuses! If they're all good I would next check the wireing on your stereo. I had a loose wire once back there and it made my instrument cluster's lights not work when I had the headlights on and I had to guess my speeds at night.
could be bad wiring