Radio turns off and wipes memory when headlights turn on
 

1989 Dodge Ram D100

It has the factory radio. The truck has 45k miles. Extremely clean truck. Nothing looks messed with under the dash, not even dust in there.
It works fine but as soon as I turn on the headlights, it turns off and wipes the memory. I turn off the headlights and it’s back on. The time resets to 1200 and it goes to the first AM station. I checked all the fuses. Nothing missing, broken, and all amps are correct. Could it be a bad ground? Where would I begin to look? Anyone else have a similar problem with a different car maybe?

First I would check for 12volts at the radio power wire with the lights on It may also have a separate 12 v source to retain the radio memory sounds like it is miss wired..