Usually the problem is in the selection of the power sources. With many cars these days what seems at first to be a switched or unswitched fuse is misleading as the car's computer alters the circuits behavior If you have a voltmeter, you can check the fuses functioning in situ. Alternately the car dealer or a stereo installation tech may be able to help you.
Much better to use proper fuse taps- wrapped wires are not a reliable connection. The ground connection could also be at fault- many bolts you see under a modern dashboard are not grounded. Also, let folks know what year and model of car this is as all will behave differently. Maybe someone else has been in your exact situation before
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