"...how could that be done?"

Unplug it. It's down around the gas pedal. Look for a relay-like plastic box with a sound hole in the top. I taped mine over with duct tape to attenuate the chime, but not eliminate it.

"...chirped up every time I touch my brakes."

As I recall, this means that both brake lights are out. When both bulbs fail, the bulb-out sensor cannot detect a current difference between the bulbs ('cause they're both zero) so it doesn't warn you.

Check the bulbs, but also check the connections where the harness plugs onto the tail light assemblies. My '83 GL sedan gave me constant trouble at that connection, and I finally bypassed the crummy design by soldering "pigtails" around the connections.

Don Foster (near Cape Cod, MA)