I don't know that the values in the link below are correct for your year, but you might pull the dash switch and clean the contacts, or replace the dash switch with a new one for your model year and T/C. A good bi-directional scanner would help you see what's being commanded vs. actual.
Switch measurement procedure here, starting at about 2:10 into it. Auto4WD = 61.7-68.1 ohms 4HI = 656-760 ohms 2HI = 1.50-1.53 K ohms 4LO = 2.32-2.37 K ohms Neutral = 1.015-1.035 K ohms Pics of switch internals. On the last pic, reflow the solder on the pins in the rectangles, and clean the...
www.tahoeyukonforum.com
Are you able to freely move the transfer case shaft to the different positions with a wrench or channel-lock pliers? I assume your T/C shaft has the two flats, and not the newer "star" end.