How does the 4x4 work?
 

Someone please correct me if I am wrong with my assumptions. When you turn the button on the dash, the transfer case is engaged by an electric motor. The front axle is engaged by vacuum. I think my front axle is staying engaged all of the time. How can I test that? Thanks.

You just about got that right....The front axle/front driveshaft is engaged by the transfer case... and the front hubs are engaged by Vacuum.

You can tell if your axle is not disengaging if

1 make sure the dash buttom is showing 2x4
2 start the truck
3 put it in park
4 put the E brake on
5 Get under the truck on try to turn the front drive shaft, if it is free turning it is working like it should, the front axle is disengaged. If the axle does not turn, then the transfer case is not disengaging the front axle, most likely the electric motor.

hope this helps

last part of #5 should say- if the driveshaft does not turn, then the transfer case is not disengaging the front axle,-or the vacuum solenoid did not disengage inside the front axle.

Nope..."truckmonger" had it right. These trucks do not have vaccum hubs. The vaccum thing is on the front differential and it disengauges the passenger's side axle shaft from the inside (spider gears).