deff sounds like your radio power is getting signal from the headlights...

i've always used the schoche or whatever adapter pigtails from wal mart, they're like $12... try that, and if it doesn't work, or does the same thing, you can just take it back...

another option would be to run the radio power wire, directly to your accessory fuse, it's how i have all the gauges/accessories in my car ran, so when you turn the key to the ACC spot everything comes on...

seems like one of those weird electrical gremlins that chase you around, but if it's always been the best buy adapter pig tails, start there, as the pins might be mixed... there's the dimmer feature on most radios, and the factory head unit, that once you cut the lights on, it dims the radio/accessories... check the pins/wiring on the adapter, not all those big box stores know what the fuck is up, and might have em crossed for their "universal nissan" applications......