4x4 switch doesn't work

check and test switch fuses relays and circuit [ harness and module ] then look under and check and test that actuator is moving

4x4 emulator motor check all fuses fist but common for motor to go bad.

Here's a link on your 4x4.Very interesting.

The adjustment of the brake light switch or it could be bad. the brake lights can work fine and the part of the switch that works the cruise doesn't The swiches that control it from the steering wheel can losse connection in a part called the clock spring. Vacume connections can effect the cruise but yours is likly cables less therefore doesn't work the cruize.

Start by checking the fuse under the dash panel. And make sure your bulbs are good. If nothing happens at all when you use the turn signal switch, it is possible you have a bad flasher relay located under the dash, the little cylindrical unit that causes turn signals to blink, and makes the clicking sound when signals are blinking. Used to be very cheap, but the newer units are a little more pricey, more sophisticated. If a new flasher doesn't fix it, then you may have a bad turn signal switch on the steering column.
The circuit for the turns goes from the fuse, up to the turn switch, back out to the flasher, and then to the turn signal bulbs.
Good luck.

check all your fuses and replace any blown ones, especially the high value ones

there could be a vacuum leak for the front diff actuator . if the actuator does not engage it will not switch into 4x4

is it while you are using your high beams, my is doing the same thing, tried wiring a toggle switch to suppement the turn/wiper stick instead of buying a new one. Worked great until i activated the momentary high beams while the switch was in the high beam position. Then power was cut to the entire car. Its like there was no batter. Can't find a single popped fuse or bad breaker, and the batter is good. Not sure what happened, according to the hanes maual i was wiring in accorance with, nothing should of happened like this.

Ive seen the motor go bad that turn it to 4 low to 4 high on the transfer case