Odd way to test system, could end up damaging 2nd module
Do the 4WD lights come on with key on and then go off, thats a bulb test?
When you select 4WD do lights flash or nothing happens?
Check engine fuse box, fuse #13 20amp, powers the shift motor
Cab fuse box #5 15amp powers module
If 4WD lights don't flash when you select 4WD then either fuse is blown or module is bad
If lights flash then shift motor is most likely the problem.
The switch itself could fail but very rare, inside the switch are 3 resistors, one for each selection, 2WD, 4high, 4low
With key on Module sends the switch a fixed voltage, lower return voltage thru a resistor tells module what position the switch is in.
When 4high is selected voltage at module changes and it activates one of TWO relays inside module
The shift motor is a 12volt DC motor like power window motor, so if one wire to motor is a Ground and the other wire is 12volt then motor turns Clockwise, if you Reverse Ground and 12volt on the two wires then motor turns Counter Clockwise, window up window down.
The two relays in the module are Both Grounds when off
Module activates one relay so one wire is now 12volts the other a Ground and motor moves in a specific direction.
Inside the motor housing are 5 contacts, the module can "read" the position of the motor by what contacts are opened and closed, so 2WD, 4high, 4low each have specific contact open/close pattern.
So module "knows" by the pattern what position the motor and transfer case are in at any given time.
So if you were in 4high and selected 4low the module would know to turn motor Counter clockwise to get to 4low, or if you select 2WD it would know to turn motor Clockwise to get to 2WD.
If you were in 2WD and selected 4high, module would power up the motor, if the contacts in the motor didn't change instantly the module would stop power and start flashing 4WD light to tell driver there is a problem
So if there is no flashing 4WD light then most likely the module is the problem or fuses
I think the 4x4 module used was the same on many years and models, wrecking yards would have that info
Tap on shift motor with hammer, lightly, lol, that can unstick the electric motors brushes and get it to work again, although it would need to be rebuilt if that works.
For future reference you should shift in to 4low and back to 2WD once a month, don't have to move the truck, just shift it, that keeps brushes clean and the gear lubed