On the stereo staying on until the door is open, either you have a wire in the wrong place or that specific stereo doesn't use the switched power to operate. I just put a new Alpine CDC-123 (well, I bought it new a couple years ago and it's just sat in a box until a month or two ago) in my Silverado which also has the key-off accessory power, and the stereo stays on after the key is shut for either 20 minutes or until the door is opened. For the dim illumination, same thing. This is one thing my Alpine doesn't do is dim with the dimmer switch, so when I find some time I'll be pulling it back out to check the wiring harness to figure out what's up.