03 GTZ - Issues With Stock Alarm

Hi guys, new to this site.. just googled my problem and saw this place- it looks like a godsend and I'm excited to spend some time on here.
Here is an ongoing issue I've been having: I own an '03 GTZ with the stock alarm system. All of the buttons on my keyless entry seem to work fine and all of my fuses look good. The problem is that after I leave the car the alarm will tend to turn on for either no reason at all or for really petty reasons like heavy winds.
I've tried to find a place to adjust the sensitivity but couldn't find one- I had the dealer check it out and they told me there is no adjustment and there's nothing they can do as far as that goes.
They did point out that there are two seperate horns- one that sits behind my bumper (behind the fog light) and one above it (behind the headlight). Both are on the driver's side of the car (I don't know if that information means anything though, ha). We figured I could just disconnect the alarm horn so as not to bother the neighbors, and just pray no one actually tries to break into the car. I was told that the bottom horn is wired to my steering wheel and the top one is part of the alarm. We even tested it.
However, the alarm would still be tripped and the horn would be set off despite the top one being disconnected. And it is the entire alarm system-the lights are flashing, etc. I now have both disconnected, which is bothersome since I am now unable to honk if someone is about to back into me or something.
Does anyone know what could be causing this or have any suggestions? I would like to have both a functioning alarm and a working horn, but could live with only having the horn.
Thanks!
-Andy

Im just guessing since my car didnt have a stock alarm, but is there a fuse for the stock alarm? maybe you could pull the fuse if there is one.
The dealer is right, theres usually 2 horns, one for stock alarm and 1 for regular horn. Maybe the dealer had the 2 mixed up? Try unhooking the bottom horn and leaving the top one in?
Stock alarm is probably only monitoring door opening and hood opening. Maybe the wind is causing it to trip one of the triggers. Maybe disconnect your hood trigger (there should be a clip under the hood trigger) and see if that is what sets off the alarm.
These are just guesses

That's a good idea, pulling the fuse.
I tested to see if the dealer had the horns mixed up and they did not.
I'll look into the hood trigger, too, that's a great idea.
Thanks for your help! I will follow up with what I learn.
-Andy

You also could upgrade to a good aftermarket alarm system.

QNZ- thank you for the advice. There didn't seem to be a seperate fuse or anything for the alarm system, but I was able to find (I think, at least- it was along the side of the hood on the driver's side just in front of where the battery is) the hood trigger and pulled it. It's been pretty windy here today and no surprise alarm adventures yet!
Bloody- Someday, when I have enough money to upgrade.... Someday.

Thanks guys! Hopefully I won't have to post here again, ha.
-Andy

You can get a prestige alarm at a pretty decent price.

Remote start w/ alarm is around $220 installed here.