I don't understand the logic of the beeps.
Today, with the car on (and ICE running) I opened the door and walked away from the car with the key in my pocket (it was only for a second to shut the garage door...homelink doesn't work all the time) and the car was silent.
Other times, I would turn off the car, open the door with the key in my pocket but do something wrong (not sure what was wrong, but the speedometer would go dark) and the car would be beeping away like I was a criminal.
Finally, I would open the door (car running, probably in gear) while sitting in the seat (to pick up a newspaper) and the car would beep.
Why would the first action not cause beeping?

The car won't beep when you leave the door open. It WILL beep if you shut it. In fact, it will beep when any door is shut while the car is running and the key is outside the car.
I believe the logic is that if you leave the door open, you are probably coming right back, so it doesn't need to annoy you. If you close the door though, it's more likely that you've forgotten to shut down, so it beeps.

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Randy