The 4x4 light is controlled not by your transfer case but your front axle disconnect fork position. So you may be in 2x4, but if that fork stays engaged, then the front driveshaft will spin as you drive down the road. The front driveshaft is not a balanced shaft, so you feel major vibes at higher speeds.
All the following are done with the vehicle in PARK or Neutral w/park brake set and wheels chocked.
1) Remove vacuum lines from front axle. Start engine and verify Jeep is in 2WD. At the axle you should have vacuum on one line, nothing on the other.
2) Shift into 4x4, you should have vacuum on the OTHER line, nothing on the first. This verifies all the vacuum lines & valves are working. Your 4x4 light will not illuminate. Turn off engine.
3) Reinstall vacuum lines onto axle. Lift and support front axle, wheels off the ground.
4) Check that front drive shaft spins freely and does not turn front wheels. This is with Jeep in 2WD.
5) Start Jeep, shift into 4x4. Verify your 4x4 light is working again.
6) Shut off engine. Shift into 2WD with engine off. Check that front drive shaft does not turn freely, but now drive the front wheels.
If all of these checks work, your system is functioning normally at this time. There are a LOT of threads of front ADD's failing. You can order a new one, convert to a manual (cable) operated one, or permanently engage your front axle. If you choose to engage it, you can either lock the shift fork into the engaged position or convert to a TJ front drive axle. You will need to get the front driveshaft balanced for either permanent solution.
'91 Frankenheep YJ. 4.0, 4" BDS, Richmond 8.8, Titan 12k, 35" KM2's, rust.
'88 YJ, 4.2/4.0 head, +4½" & shackles, BFG 33's (sold)