I would assume that the seatbelt buckle has 2 contacts on either side, and when the seatbelt clicks in it completes the circuit. Because the light has been off mostly, I would assume it might have shorted to ground somewhere before the seatbelt buckle.
This is if my assumption about how the circuit works is correct.
Otherwise the seatbelt may push a switch down inside the buckle which would be a normally closed circuit in which case you would be looking for a broken wire pre or post switch
Pull the plug under the seat and check both wires (I''m pretty sure its a 2 pin plug) With the car on, one should have power and no ground, the other should have ground and no power.
If its a 1 pin plug then it should have power at the wire and no ground and it must ground through the buckle and seat rail so check there is a good earth from the seat buckle bolt/nut to a good chassis earth
This is all assumptions remember, Hopefully helps. Good place to start anyway, as the plug is easy enough to get to and you dont have to pull things apart