Its not that simple to troubleshoot. These auto transfer cases are a little more complicated in that the motors are PWM with a position holding brake circuit along with rotation hall effect sensors. The motor spins both ways, depending on the polarity applied. You would have to make sure the brake is released to see any movement. You are probably seeing the transfer case motor incremental sensor which will read 0.75V or 4.2V depending on the position. It will bounce around as the motor rotates. The controller provides a 5 volt reference signal. The separate position sensor will vary between 1.8V and 3.6V. The voltage feedback from the motor brake is either near 5-8V or near 0 depending on the controller wanting to rotate the motor. So if the motor is seeing 11v and the incremental sensor is not changing, it kinda sounds like the controller is trying to rotate the motor but nothing is happening.... but thats just a wild guess.
There have been a couple recent transfer case issue threads, with clicking actuators. Here is one that turned up in a search:
http://www.jeepforum.com/forum/f309/2012-laredo-5-7l-v8-transfer-case-issue-4313371/
You are really flying blind without being able to read the drivetrain control module and cabin node codes. Its the only way to efficiently troubleshoot short of replacing components on speculation. The scan tool also allows the tech to command functions so the reaction can be observed.
When you say module, do you mean the control module under the rear quarter panel trim, or the transfercase? The control module itself needs at least 8.5 volts from the battery.
You will find most of the time this kind of problem turns out to be a transfercase replacement or control module replacement or both the controller and actuator (one burns the other out). Sometimes the position sensor. Sometimes its a data bus thing, where a misbehaving module throws noise onto the data bus. Intermitents are loose or corroded connections most of the time.
I don't have a 2014 circuit diagram handy. You can get a three day pass to FCA's technical data base, which includes FSM type data and more, for around $35. They usually have pretty detailed info and info specific to the 2014.
Your symptoms are a little different in that you don't seem to have a locked up transfer case and they are intermittent... have you checked fluid levels as low fluid can cause sticky shifting? Have you tried switching between terrain modes? On second thought... that may lock you into 4WD

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