check fuses for the 4x4 system
After that I would plan to rebuild the shift motor
98% of the time in the last 25 years of fixing the ESOF 4x4 systems, the shift motor is 98% of the time the problem
On a 92 explorer there is a plastic spacer inside the rotating assembly inside the motor. The plastic deteriorates and will allow the motor to over travel. = no lights, no response, no nada
By taking it all apart, cleaning the insides and replacing that spacer it usually works like new again. I use a piece of clear plastic tubing to make a new spacer.. Mark the stator body to the lid before taking it apart so you can keep alignment when you put it back together. You will see hash marks if you clean it well enough, so you know what I am talking about
FYI the old motors like yours can be rebuilt many times over their lives as needed and continue to work.
I had my original 1988 shift motor until 350K miles....took it apart and cleaned it about 3 times before I finally converted to manual t case
I have fixed many many many shift motors over the years simply by taking them apart, clean, lube and put back together.