Searched the fora here and found a number of threads talking about doors/lids/cas caps being left open, but that doesn't seem to be what this is. My 2001 360 beeps once on lock, and twice on unlock. Just tonight it started beeping three times on unlock. No idea what that means. Checked all the doors and lids and so on, nothing is open. My car didn't come with its manual set, so hoping someone who has one can tell me what this means. (Also, does the car alarm sometimes randomly turn itself on? When the car's recently used and still ostensibly unlocked, I'll sometimes get a loud beeping alarm when a door is opened. Usually it's fine though. So I've taken to locking and unlocking it with the fob now before opening it, even if it SHOULD be unlocked, lest I wake the baby or something...)
Doors and lids being closed doesn't mean the latch/lock switches are sending the right signals. Sit in the car with everything closed and turn on the ignition. Is anything indicating open on the dash? The gas cap lid isn't part of the alarm system. It should only go into engine immobiliser mode by itself when unlocked, not alarm mode. Not sure why it's doing that. When you go for a drive, is the alarm LED still illuminated? The usual suspects are expired battery in the siren and issues with the anti-lift sensor. The siren can use the car's battery, assuming the battery hasn't leaked and damaged the siren's circuit board. How old is the car's battery? Do you have the car on trickle charger when not being driven?
Michael- As mentioned, sounds like your siren has gone. Mark (ferrarifobs.com) has new GM sirens that have been reflashed with Ferrari software. I have one in mine and it works perfectly. An SD2 or equivalent may help you diagnose the problem in case it is something else.