One thing, it may not just be as easy as plug-and-play. Some piezo elements require a driver (some have integrated drivers as well). The driver uses PWM to rapidly oscillate the element and vibrate, causing the sound.
RadioShack has a bunch which have internal drivers and would work on a wide supply range. These should be a relatively easy drop-in for the one in the FJ (although, I haven't looked at it to see if it's something custom, I doubt it's anything more than a regular piezo buzzer).
The reason I say that is the buzzer may be triggered by 12V (most likely), but it could also be triggered by 5V off a signaling line from something. One like
this works with 4-28VDC, covering anything in the range. It might be worth it to find the buzzer and put some volt meter leads on the pins first just to see what voltage level drives the piezo.
I wish you luck -- my uncle has had the same thing happen from too many records through headphones, too loud!
