I'll guess that the on/off switch to the lamp is wired on the ground side. Somebody didn't know that, and tapped the amp into it. When the switch is open, 12v is available through the lamp (in series) and is enough to run the amp. When turned "on" that side becomes ground, and the amp gets zero volts. If my hypothesis is correct, removing the light bulb will also disconnect power and kill the amp. Just a guess! (in many 12V circuits, black is ground, but in 120 vac, black is hot.... could be part of some confusion???)
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