I attached the description of your transfer case. If it is not engaging then I would expect the clicking is coming from the encoder motor trying to turn the actuator but it is not able to. So it is either the motor or this assembly. The best way to figure it out is get in there and monitor the operation. I included the procedure for replacing the encoder actuator which will get you into the entire system.
Unfortunately, there are no magic bullets for this one. You will just need to test the motor and then inspect the actuator and lever to see if it is able to move.
Read this over and let me know if you have questions. Thanks
Images (Click to enlarge)
Wednesday, May 8th, 2019 AT 7:09 PM