Just chased this problem down on my 70 GTO. Turned out I had tapped into the unused glove box light positive wire for my stereo constant wire. I just undid that connection. I have yet to decide on a resolution as now my stereo keeps no memory because of this. Factory stereo did not need a constant 12v supply because there was no clock in it.
This might not help you any but, sometimes it's nice to know your not the only one out there chasing electrical issues. Good luck.
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