If I remember right, on my Gen 3 the wire going to the release from the button is the negative. So when you push the button you are completing the negative side of the circuit. I am almost positive about this because my alarm system only has a negative trunk trigger. You would have to find the positive side of the circuit and run it to something that is switched by the ignition.
Why couldn't you just switch the positive wire from +12V always hot to the +12V ignition hot? Just re-wire using the ignition wire off the back of your stereo. This would require the car to be either running or in ACC in order for the trunk to open via the switch. It won't get power until then and won't pop unless, of course, you push the button to complete the circuit.