What I am getting at is to make your system work with a controller, just like the rest of the ACC based ones.
Something tells me that your car, just like mine, has an illumination around the ignition key. This is where you need to tap in. I am hoping it is positive wire based and not the negative one, otherwise a relay would be needed. A voltmeter can be used to determine it.
If it is positive based, all you need to do is to wire 1 diode from the positive wire to the ACC input of the controller board. Another diode, placed the same way, needs to be wired from the ACC wire to the ACC input of the controller board.
If you unlock your car and get to it before the dome light turns off, controller board will keep thinking the ACC signal is present. Then, when you turn your key, it will provide ACC and override dome light input.
When you turn off your ignition key, normal shut-down sequence would initiate.