The pictures posted are of the reduction gears not the motor, the cover plate with the 4 or 5 wires, over the larger gear, are for the "contacts", which are, in essence sensors, for the control module, and do not power the motor, they "tell" the controller the position of the larger gear, which would be the position of transfer case shift rod
The electric motor is the black cylinder and its Brushes are the usual problem when you have intermittent issues
Motor is powered by the 2 wires that enter the housing at a different location from the others
Picture here of housing with electric motor removed:
https://therangerstation.com/tech_l...ilding_a_ford_transfer_case_shift_motor-4.JPG
Brushes seen hanging
Picture here of the Rotor contacts for the electric motor, these need to be cleaned:
https://therangerstation.com/tech_l...ilding_a_ford_transfer_case_shift_motor-8.JPG
Picture here of the brushes, springs and holders:
https://therangerstation.com/tech_l...ilding_a_ford_transfer_case_shift_motor-9.JPG
The springs go into the holders first, then the brushes, when assembled, the springs push brushes out to hold them in contact with the Rotors contacts
This setup allows the Rotor to turn while maintaining an electrical connection, all electric motors operate this way, except "brushless" which are not available for these shift motors.
Picture here of the brushes, springs and Rotor in place:
https://therangerstation.com/tech_l...lding_a_ford_transfer_case_shift_motor-13.JPG
The brushes can get stuck so spring can't push it down, or spring can break so not enough force to hold brush against the Rotor.
Rotor's contacts can get corroded so voltage doesn't transfer between brush and Rotor