Head lights on alarm/dinger?

Does it chime when you leave the key in or don't buckle the seat belt? For the headlights it should sound when the lights are on, the key is off, and the lights are on.
If you hear the chime for key left in or the seat belt it isn't the chime. The chime is part of the central timer module aka the body control module in that truck. The power for the CTM also powers things like the door locks, wipers, and others so it's not going to be a fuse.
Do the interior lights come on when you open the driver's door? To diagnose it you will need a DRB III scan tool for testing and to program it to match your vehicle if you need to change it.