Lights control the radio?

It sounds like the battery power wire (for the deck) is connected to the accessory source.
And the accessory input for the deck is connected to the dimmer wire.


IIRC the car's accessory wire is yellow/blk
Lt green/Yel is the memory power source.
The dimmer is or/blk or something along those lines.

If you test each wire with a DMM or test light, you can narrow it down real quick. The wire that's hot with the key off is the battery source, the wire that's cold with the car off but hot with the key at run is your accessory wire, and your test light or DMM will go down as you turn the dimmer down.

Good luck.