Unfortunately on that body style I think the buzzer box may be connected to the back of the instrument cluster. And if it's anything like the earlier generations, you'll lose some other random functionality if you just unplug it, like dome light and seatbelt light. You have to find the box, crack it open, and actually disable the buzzer.

My Truck: 1987 XtraCab DLX 22R 4WD 5 Speed Manual
--------------------
"Speed has never killed anyone. Suddenly becoming stationary, that's what gets you." -Jeremy Clarkson