Hmm, not going from anything I really know for sure here but...
It sounds like the light turns on when a button gets pushed (or let off) some where on the door handle, or the latch that it opens. Obviously not from the door opening. Still, I think there is a push button switch that is opened while the door is open, too. Take the interior door panel off and look for wires and try to figure out where the switch is that gets activated when the door handleis pulled.
If the button is let off when the handle is pulled then cut out the switch and attach those two wires to get a constant circuit. If the switch is pressed down to complete a circuit I don't really know what you would do.. I suppose you could cut the power wire from it and cap it so the circuit never gets completed.
Also, when you locate that switch you can always just like relocate it or something so it isn't activated w/ the doors.
To be honest this is all me speaking from what makes sense to me. There may not be a switch or any of that crap. Just an idea, since I don't have an Alero to test it out on or poke around in.
Best of luck.
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