it is the alarm
I have the same car 2003, 330i.
I was at the dealer 2 weeks ago and asked the same thing.
I was told that the car does nto come with the alarm, it is like a $500 extra.
Even though I have the Red light under my rear view mirror, the car does not have the alarm.
Without the extra alarm option the red light does not flash, and there is no audible sound when lockig the car.
This seams odd to me, why would BMW put a non function red light under the mirror?
Anyhow that is what I was told.
Possibly someone else can confirm who knows for sure.