Alarm System Issues?, Seems to be killing my battery periodically...? Options

[Kaiser]

Guys, I need some help here. When I first bought my Celi, the guy explained how its alarm system worked. Apparently it used to have a horn, but he "cut that out." So instead, it just ticks until you hit the button. I mean, I don't know how many other Celicas were equipped with the same one, I assume it was a dealer install? It's got the little button down in the footwell that you have to hit before you can start the car, and it goes off any time you open the doors or hatch or anything and can't be deactivated unless you actually go as far as to start the car (if you just push the button, it comes back eventually?)

So it seems that it's killing my battery. Every once in a while I would go to start the car and the battery would be dead; I was only starting the car like every week or so back then, but the battery is basically new, so I wouldn't think it would die off that quickly. I haven't noticed anything else that would be causing a parasitic drain, especially considering the lights would all start flashing even when I opened the door to get something out of the car and would stay that way for a good minute or two. What can I do to fix this? Does anyone else know what I'm talking about at least?

I like that the alarm stops anyone from starting the car up unless they know where the switch is, but if my battery is going to suffer, I just can't keep it. Is there an easy way to disarm it permanently, or at least alter it so that it doesn't keep draining the battery? My car's in the shop right now since I was changing the timing belt and valve cover gasket, so I figured now is the time to get anything else done that it needs. Anyone have any advice?