You can start by disconnecting the turn-on, power, and ground leads from your head unit, then switching on the headlights to see if the "bulb out" indicator goes away.

The "bulb out" principle works on measuring a fixed resistance, and a bulb that's out in the whole circuit sends a different resistance value, thus triggering the "bulb-out" light.

So if you happened to splice into that circuit, the presence of the head unit would certainly cause the same effect...

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car