Sounds like there's something wrong in one of the switches (possibly the key-in-igntion switch) like Grampy_Jim suggested.
To silence the key-in-ignition dinger, you can pull the black/pink wire out of the 6-pin connector just to the right of the steering column under the instrument panel. That won't take care of the headlight dinger though.
You might be able to pull the white/red wire loose from the headlight switch plug, but I haven't tried that.
For the seatbelt dinger, you can just unplug the connector under the driver's seat.
On edit: Not sure this will work on an 01 truck. If it has a GEM, it should work.