Problem...the unit won't shut off. Wired it correctly. While holding the AV button in, the unit display is still on after the car is off and keys out of the iginition, and alarm set. I hold the "V" button in and the display turns off though the lower display buttons illumination is still on and the machine is making noise.
Yah, you don't want to leave it in that mode. The Z1 is still on and it draws 1.5 - 2 amps at idle. It will drain your battery in just a few hours.
As I don't want to drain the battery, I pull the factory radio fuse. Not sure if there is a certain amount of time after departing the vehicle that the VW's power completely turns off?? Or if the Pioneer Z1 unit takes awhile to cool down before shutting down??

Good idea... for now. The Z1 will turn off immediately and there is no cool down time. It should should off immediately.
Problem...the unit won't shut off. Wired it correctly.
You say so, but you either didn't wire it correctly or the instructions you got with your harness are wrong. Either way you didn't wire it correctly. You might have wired it as the instructions from your harness said, but they could be wrong. I don't have any experience with that harness or that company.
The yellow wire from the Z1 needs to be connected to battery positive. The red wire needs to be connected to switched 12V. When the red wire sees 12V it will power up the unit and draw power from the yellow wire. If the red wire goes to 0V when you turn off the key then the unit will shut itself down.
It sounds like the red wire from the Z1 is connected to something that has power that never goes away.
Check the yellow wire and the red wire on a volt meter. They might be reversed (I have no idea what that would do to your Z1, it could be bad or could operate like this). But either way, it sounds like the red wire from the z1 never goes to 0V. Check those 2 wires. I'm thinking you did not wire one or both of those wires correctly.