your chime module is bad. it controls the light and buzzer. physically buckling the seatbelt disconnects the ground circuit to the buzzer half. so it kills the buzzer but not the light.
its located by the fuse box under the dash. as a test pull the module and the light should go out.
TEST
DIAGNOSIS
If the buzzer/chime unit does not operate as described, check the two fuses for pins 1 and 7 (Figs. 1
and 2) and replace as required. If the fuses are not
defective, perform the following tests to determine if
the problem is in the module or in the wiring. Using
a flat head screwdriver, release the locking plastic
clip while carefully pulling out the module. Plug in a
known good module and check its operation. If the
problem is not corrected by replacing the module, remove the module and continue as follows:
VOLTAGE TESTS
Ignition in ON position, measure between the
following pins and vehicle ground.
† Measure voltage at buzzer/chime module connector
pin 1. Meter should read battery voltage. If not, repair open to ignition switch.
Turn ignition OFF and remove the key from the ignition.
J CHIME/BUZZER WARNING SYSTEMS 8U - 1† Measure voltage at buzzer/chime module connector
pin 7. Meter should read battery voltage. If not, repair open to fuse.
RESISTANCE TESTS
CAUTION: Before using an ohmmeter, turn ignition
switch OFF and disconnect negative cable from battery to avoid damaging the meter.
Measure between the following pins and vehicle ground.
† Buzzer/chime module connector pin 2. Meter
should read almost zero ohms (bulb filament). If not,
replace seat belt indicator bulb.
† Buzzer/chime module connector pin 3. Meter
should read zero ohms. If not, repair open to ground.
† Buzzer/chime module connector pin 4. Drivers seat
belt not buckled. Meter should read zero ohms. If not,
repair open to ground (or buckle switch may be defective). Meter should read open circuit if drivers
seat belt is buckled. If not, repair short to ground (or
buckle switch may be defective).
† Buzzer/chime module connector pin 6. Open driver’s door, key in ignition (in OFF position). Meter
should read zero ohms. If not, repair open to ground.
† Buzzer/chime module connector pin 6. Remove key
from ignition. Open driver’s door, headlamp switch
ON (except YJ), meter should read zero ohms. If not,
repair open to ground.