The motor only has two positions, high and low. If it is in high, that is the same position it would be in for 4hi/auto.
The motor does not ground through the case. Which high/low position it is in is achieved by reversing the polarity of the power wires going to it, making one positive power and the other ground to switch one way, and then reversing their polarity through the Shift Control Module to make it shift to the other high/low position.
Both of those wires are normally grounded, then the Shift Control module switches one or the other to 12V depending on which way it is supposed to shift.
It will only receive power for the moment it is changing position. You can check whether the Shift Control module is outputting this power. It's in the dash, behind the radio IIRC. The orange and yellow wires are the two which power the shift motor and reverse polarity.
You should also check the Shift Control Module's connector black wire, resistance to chassis ground, should be near 0 ohms, and there should always be 12V on the dark-green/light-green wire to it. If there is not 12V on that wire, or perhaps the first thing you should check instead since it's easier, is the fuse #6 in the under-hood power distribution box. See circuit diagram attached.
If the Shift Control module is getting 12V on the dark-green/light-green wire but not outputting on the yellow and orange, then I'd use a multimeter to measure the resistance the dash shift switch module should have in each switch position as shown on the diagram, that it should have between the white/light-blue wires and gray/red wires in each position (approximately): 3.9K, 1.1K, and 360 ohms.
If you wanted to test the shift motor directly, you could unplug the connector to the Shift Control Module, and apply 12V to the yellow and orange wires for a brief moment. Make one of the wires positive and the other negative then do the opposite, making the other wire positive and negative.
With the motor detached, note which position it is currently in first, then you should have it shift at least one way or the other if not both, then remember to shift it back to the position that the transfer case is in which you reported as being high mode right now.