But since I am in a " Class in session " mood
Here is a description of how your system works. Most likely the shift motor, GEM or switch. See highlighted.
Edit added another highlight
The Automatic Four-Wheel Drive (A4WD) system is an electronic shift 4x4 system that allows the operator to choose between three different 4x4 modes as well as Two-Wheel Drive (2WD) . The operator can switch between 2WD, A4WD, and 4WD HIGH modes at any speed. To engage or disengage LOW range, the vehicle speed must be less than 5 kph, the brake depressed, and the transmission must be in NEUTRAL.
In A4WD, the Generic Electronic Module (GEM) varies the torque split between front and rear drivelines by controlling the transfer case clutch. The transfer case clutch allows for slight speed differences between the front and rear driveshafts which normally occurs when negotiating a corner on dry pavement. When the rear wheels are overpowered, the GEM detects this slip condition, and the duty cycle to the transfer case clutch is increased until the speed difference between driveshafts is reduced.
The 4WD mode switch is a rotary switch which allows the vehicle operator to choose between 2WD, A4WD, 4WD HIGH, and LOW range positions.
The Vehicle Speed Sensor (VSS) , mounted on the rear of the transfer case, informs the GEM of vehicle speed.
The Hall effect sensors, mounted to the transfer case, are used to detect the speed of the front and rear driveshafts.
The electric shift motor, mounted externally at the rear of the transfer case, drives a rotary cam which moves the mode fork and range fork within the transfer case to select between the 2H/A4WD, 4WD HIGH, and LOW range positions.
The shift motor sense plate, an integral part of the electric shift motor, informs the GEM to the position of the transfer case.
The Transmission Range (TR) sensor, located on the left side of the transmission, informs the GEM of the transmission gear position.
The Expedition/Navigator is equipped with 2WD and 4WD vacuum solenoids attached to the upper RH side of the engine compartment dash panel, they alternately route vacuum to the vacuum motor which engages/disengages the center axle disconnect collar in the front axle assembly.
The 4x4 shift motor relay is a module containing two relays which, under the control of the GEM, shift the transfer case shift motor between the 2WD and the three 4WD modes.
The solid state clutch relay is used to activate the A4WD clutch within the transfer case