Most cars (your 94 burb also) don't let you take the keys out. Modern cars anyway. GM's one-side keys wear out after a while and eventually allow you to pull the key while the engine is running. But that isn't exactly a built in feature... it's more like an accident.

The lock-in feature of the key is built into the lock mechanism itself. Although there could be a way to fix it so it doesn't work anymore, you would probably have to disassemble the entire ignition lock and that is getting into specialized territory.

If it depends on the door opening and closing to "think" you left the car, just open and close the door, and wait for it to turn off. Or will that set the alarm off when you go to leave the car for real? Also, will it disable the remote start if you turn the key to "off" and pull it out of the ignition, using the manual trans feature of the alarm? That way, it wouldn't work at all obviously, to try and fool it into thinking you've left.

You COULD always use two keys. Leave one in, shut the door, then open the car again and remove the key after it's shut off. That sounds like a royal pain in the ass, and it would also not work if you disabled the remote start by reentering the car and removing the key.
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1992 940 wagon, low miles
as well as others.