2001 Pontiac Grand Am switched power

I have a 2001 Pontiac Grand Am GT. I have installed a Satellite radio. Everything works fine, except I am trying to wire the power to come on and off with the Ingnition. When I probed the wiring harness I found the Green wire to have 12V when ignition is on. When the Ingniton is off the power would switch off after about 40 seconds. I thought I was done. The radio will also come on when I use the keyless remote. It comes on for about 40 seconds and goes back off. Does anyone know what wire in the harness I should have connected to, or where I can find true switced power? I thought I tried all of them, and I probed them whe the harness plugged into the radio. Thanks.

Just go to the cigarette lighter then.  My ex once told me I have a perfect face for radio.

The cigarette lighter power is constant and dosen't go on and off with the ignition.

Can't you run the wire to the "radio" fuse in the fusebox?'85 Toy

I tested several fuses, including radio and interior lights. With the ignition off they all have 12v on them. I am not sure what is going on, but I think there is a constant 12V and also a signal to tell the radio, lights, or other accessories to turn on and off. Does anyone have any ideas?

The radio harness does not have a switched 12 volt source for power. The radio turns on and off via a data message from the BCM. Use the thick brown wire off the ignition switch. This is the accessory wire for the car, but it won't work with the ignition off and the doors closed (retained accessory power). The green wire you tied into would be the radio on circuit used to power the antenna module and amp if equipped. sparky

Thanks for your help, I'll try that!