The only thing that usually causes that is a bad radio (or a radio with bad firmware, which in the case of an aftermarket unit, you have no control over). If something in the truck is waking it up then it has to be the Acc input, but the thing is, unless that input is continuous, the radio should go back to sleep. To eliminate the possibility of stray voltage building up in the Acc circuit and tripping it, put a pulldown resistor on the yellow wire. A 3.3K 1/2 watt should suffice, something like this:
Resistance Value 3.3k Ω ohm. Carbon Film Resistors. Type Carbon Film. Quantity 10 Pcs. Give us the opportunity to make things right. I try to take the best pictures I can to show the item from multiple angles.
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T-tap the yellow wire and connect one end of the resistor to it, then connect the other end of the resistor to a chassis ground. That will supply a "hard ground bias" to assure that when the Acc relay is open, the line will go to 0V and stay there. With that in place, if the radio still wakes up when it shouldn't, it's either a bum radio or there's something external that can wake it up that you're not aware of, like a bluetooth or WiFi link.