2002 Cavlier dome light

You do not need the positive door trigger input to the alarm when your car has negative door triggers, except in special cases (like Astrostart Alarm starters)

As far as adding dome supervision there are a couple of things you can do.

1) use the door trigger. The dome supervision should come on when you unlock it, so your alarm will be disarmed anyway. I don't believe that cavaliers door triggers are directly responsible for the light coming on anyways. That is to say that the door trigger sends a pulse to the bcm, and the bcm turns the light on. So using a door trigger should be ok.

2) If you still don't want to use the door trigger, you can use a relay to break the ground wire at the dome light, and feed it a ground to turn it on. That would go something like this: 85=12v, 86=dome supervision output from the alarm, 87=ground, 87a=domelight ground (car side), 30=domelight ground bulb side. I would make a diagram for you, but I am at work and time will not allow me to do so. You should be able to figure this out tho.