I have this same noise... I'm going to mess with it tonite on my drive home from work. Mine does it at idle, like at a stop light or somthing, AND while driving. I sure hope its that peice by the windsheild.
ok - i am for dead sure now that the chirp is coming from the wiper cowl. i can duplicate the noise EVERY TIME when the car is parked, by just pressing gently, and kinda rapidly, on the cowl near the passenger wiper. i have spent a LITTLE time trying to see how easily the cowl can be removed, and have even shimmed (crammed) a small sliver of pool floatie foam underneath it. that helped a LITTLE.
funny - when i raise and prop my hood, i can't make it chirp. something must be getting tight, or binding, in that process. can't drive with the hood up, though.
i wish you luck, my fellow mustang driver, in your quest to eliminate this chirp - this ICE PICK IN MY BRAIN. please alert me if you find a good remedy.