It could be the Encoder/ motor not shifting it properly. I have had to replace mine. as it was having trouble seeing what position it was in. You may also want to check that the Front differential is engaging.
What I would do, is with the key in the on position and vehicke NOT running, have someone rotate the know while you are underneath the truck. in Auto, you will hear the front differential lock in place and the transfer case shift to auto mode. then go to 4 high. should hear the transfer case shift again. then go to Low. I think the (truck needs to be in Neutral).
Turn the volume up here. this is my truck. First noise is the 4 Auto, then 4 high, then 4 low. then it goes back. I have the NVG case, you may have the Borg Warner case but they should produce similar shifting patterns.
https://www.youtube.com/watch?v=fNVWlQxC-1M
If your encoder motor is not operational, it is a pretty easy fix. I just ordered the part off amazon and I believe 3 bolts and a plug and it was out.