I found why such thing happens.In the front of the car, by the passenger headlight there are 2 plugs that the main engine harness plugs into. One is grey and one is brown.
On the grey plug, there is a black and white wire that needs to see switched 12V with the key. It looks like your car is not cutting the 12V to that wire when you take the key out.You have 2 choices, you jump the black/white wire on the engine harness end to the black/red or you chase the black/white wire to the relay that powers it and see what the problem is.
If you cut the black/white wire and connect it to black/red it will fix the problem. I have not see any overdraw problems if running the car this way.Good luck and keep us posted.
ThanksYury Lyalkohttp://
www.wiringspecialties.com