It's a simple device to test. A low air condition causes battery positive to be applied to the single wire going to the buzzer box, and it is grounded via it's case. Drain the tanks down, flip the main switch on, check for power at the wire to the buzzer.
If power is not present, check the switch for power in, then you can chase down the wiring/switch issue for no power in, or you can condemn the switch if it's not "switching" that power that's available to it.
If power is present at the buzzer, verify the ground path (apply power to the buzzer wire and check the case with a test light, should NOT show power), and you can either repair the poor ground path, or if that's fine then you can safely condemn the buzzer.
Lots of folks unhook them, I'm OK with that since this is really here to assist the brakes, it's not like full air where an air failure causes no brakes at all. Personally however I kind of like having it there. If nothing is wrong you'll only ever hear it just after startup.