The alarm was an extra on the bmw, but not sure if you would have the light but bmw do silly things like put in the parts but dont connect them unless you pay, so either you have'nt got an alarm connected but does sound odd as you have the light but like i say it was an extra and std you have an immobiliser or somewhere it is disconnected or a fuse something like that, as the red light should be flashing when locked up but you cant see it flashing in daylight as so dim but at night in the dark you would. If you have the handbooks still have a look in there about the alarms, if not i have all the handbooks but will have a look, although mine is on the dash but i have a 2001 728 sport just before the new shape.