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I would pull the shift motor and plug it back in, then try using the dash switch to change its position
No "click" noise from 4x4CM(control module), behind radio, and no flashing 4WD lights on dash, would seem to point at a 4x4CM issue, not shift motor issue
Then pull the shift motor out, take it to battery and apply 12v and ground to the Orange(brown) and Yellow(grey) wires, the 2 wires that go to electric motor
It should move, reverse polarity and it should move the other way
If so shift motor is OK
The system only has 3 parts
The dash switch, which never breaks, just 3 resistors inside
The 4x4CM, behind radio in 2011, known issue
The shift motor, these do fail from disuse, should be used once a month just sitting in driveway
When the 4x4CM gets a voltage change from the dash switch, it close a relay inside(the click) to send 12volts to the shift motor
If the shift motor doesn't start to move instantly, 4x4CM will start to Flash the 4WD lights on the dash, indicating a problem
Could be shift motor fuse or shift motor itself
If there is no "click" and no flashing 4WD lights then first stop would be 4x4CM not the shift motor