random chirping

I’ve got a weird alarm problem, the car (99 355) sits in the garage, unlocked, battery tender hooked up, and the alarm siren chirps randomly, like a wounded sparrow. It may take a week or so to start this random chirping. If I open the deck and leave it open it stops, or maybe it was opening the door to release the deck that stopped it, but in any case when the rear deck is open it hasn’t chirped.

Alarm siren module was replaced last year with the 360 module, the one with the two green batteries.

Any thoughts on this?

I'm thinking to power the siren from the main battery, but I need am electrical guru to tell me how to cut the voltage down.