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There are wires in the aftermarket wiring of the radio that are jumping power somewhere.Chris Lucas73-87chevytrucks.comcaptkaoscustoms.comsquarebody.biz
if you have a test light with the key in "off" position test the red wire coming from the radio and see if it has power, next check the yellow wire. the red should not have anything. the yellow should have low voltage because it is a memory wire. if your red wire does have power pull the radio fuse as you stated before, if that still doesnt kill the power you will need to start tracing that wire back and see where the hickup is
does your radio have a dimmer feature for night driving? could this be wired into the trucks headlight switch so when your headlights are on it dims and that wire is somehow powering your stereo?
Using a test light, ignition off, and radio harness connected to radio, which wires are 12 volts hot - probe the ground wire, as well? Check again with the T/L CTSY fuse removed. Post the results.
Just to make sure we are on the same page, your radio should have accessory power (some installers substitute ignition power) to turn it on, and constant battery power to maintain memory. The "tests" I described should be sufficient to determine whether the fault is internal to the radio.