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I bought a cheap Ebay radio. The radio harness don't have a blue white wire that connects to the BLUE wire on the Pac roem-vet1 harness for my 2001 C5 corvette.
The system plays but you can tell the amp doesn't work.
You could probably run a switched power lead to the PAC harness blue wire, that will give it power when you turn the car on, or you use a splice connector and run it off of the switched radio power wire, that will also provide power when you turn the key or radio on, I would install a inline fuse on this connection, I don't think you would need it but just to be safe, if I'm understanding what your saying correctly this should provide the power signal needed to turn the amp on. All you need is to provide a switched power signal to the blue wire so it knows to provide power to the amp.
My understanding is that the blue wire is the trigger to turn on the Bose amplifiers and it is supposed to connect to the amplifier trigger wire from the radio. If you don't have an amplifier trigger wire then you can connect it to the same place you connected the red switched power wire from the harness.
You could also just tie it together with the switched or keyed power lead in the harness to radio wires which should be a red wire too.