I have a 98 Oldsmobile Bravada the service 4 wheel drive light is on and I hear a clicking noise in the glove box when starting

Check fuses.
scan the PCM yet?
1998
4wd is

computer controlled NP-136 transfer case, which works more like traction control. The Bravada was now run in RWD in normal operations, and only when wheel slip was detected did the SmartTrak engage AWD


The NP136 transfer cases was manufactured with electrical shift encoder motors, this unit has two different drive ranges 2 high and 4WD (run at reduced speeds) with the front output drop on the driver side. This unit has a 27 spline front output and utilizes a rear slip yoke.

if you have purchased your car used the very first order of business is to double check the tire diameters.
Used car dealers may have mismatched size the tires to make the sale. Mismatched tires will cause the NP136 transfer case to fail.The NP136 transfer case unit has a couple of problems, it utilizes a viscous coupler clutch system that can fail. One way to recognize this failure mode is clicking sounds when turning on dry asphalt or concrete surfaces. Viscous coupler failure is attributed to excessive heat build up. The second problem is that the oil circulation pump on NP136 can wear a hole in the case, we provide a transfer case saver to prevent this from happening. Once you have a hole in the case fluid will be lost and the case will fail. Don't leave home without our case saver, it's only a matter of time. Recommended fluid for the NP 136 transfer case is GM part number 12378396.

and more
get the car serviced, or learn to scan first. and post DTC seen