Chevrolet Repair Questions? Ask a Chevy Mechanic for Answers ASAP
This is not normal and indicates a possible issue inside the radio. When you have the lights on it's getting a power feed from a different location then when the lights are off. You may be able to tap on the dash and see if you can make it happen,but it sounds like the radio itself is the problem. If you are still under warranty, get it back there.
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