Just another thought, when you removed the Bose from this car how did you re-route the outputs? Did you use a none Bose turnaround connector? The switched 12V for the rear audio components is derived from that connector.
The speaker output wires in the loom at the back of the stereo Have a black tubing around them
The Bose units use these 8 wires to send a pre amp signal to the Bose amp
And then the Bose amp sends the amplified signal into the same colour co-ordinated wires in to the speakers
All I did was to couple the wires to the same colours
For the front speakers
And for the rear shelf I connected the the wires direct to the speakers
That’s left me with three wires
Power red
Ground brown
And 12v signal red/white
I just insulated them