Does the Mini's OEM alarm system include motion sensor for all mini coopers installed with the factor alarm or is it just for those with the convertible?

I just bought a 2005 Mini Cooper, not convertible and had BMW in Long Island New York install the alarm for me.
I'm not sure if I have a motion sensor. I tried rolling down the windows, waiting 30 seconds and waving my hand inside from the window, no alarm., However, when I attempted to open the door from the window, the alarm went up. Where are the sensors located. I noticed that the interior lights looks as if there is a sensor located on the right and left side of the bulbs.

I also wanted to know what is the box-shaped item on the interior roof of the car, situated in the back? It has vents.

Thanks in advance

 

Therein lies your answer.
The motion detector is in the box - it's a small black thing with two horn shaped appendages.

As for the motion sensor, I've heard two conflicting stories.

1) Test by your method
2) That the motion detector is disarmed when the window is down, which would make 1) impossible. (i.e. the motion sensor is designed to go off if someone breaks your window.)

I didn't bother to do any more research.
You may want to pop into the dealer and see if they can unravel the mystery.

 

If the alarm is on and there is movement inside the car, the alram will go off. You can shake the car and the alarm will not go off, but if you hit the car (someone backs into you etc.) The alarm will go off.

For instance, my sirius sat rec, which is suction cuped to the windshield) came off the other day and fell. That triggered the alarm. Windows up or down on my car does not make a difference. Mine is a '04 with OEM delaer installed alarm.