Did you change your passenger's seat?
Those seats may have a weight sensor that tells the Sprinter to beep when there is a passenger.
(but the 2004 wiring diagram doesn't show one, see below)
On the other hand, my 2005 has beeped no matter what: one person or two, belt(s) connected or not, since brand new.
Here's the 2004 wiring diagram, it shows the seat belt switch as a fairly simple "connect-to-ground"
(and doesn't show a switch for the passenger side at all... perhaps that's the root problem)
My
guess is that the switch needs to be closed to satisfy the beeper.
The Instrument Cluster beeper is the same noisemaker used for all other functions, so if you like to hear that you left your key in when you open the door, or that the headlights are still on, you don't want to disable it completely.
--dick