The difference between UD & OD is in the gears. The housing, shift mechanism, etc is the same. The only way to convert one to another would be to swap the entire gearset, which means finding a good set of OD gears. These are helical and the input/output gears and integral with the respective shafts so there is no way to swap them around. From a practical point of view you're best bet is to find a complete box with the correct gearing.
I am unclear if you have an UD or OD. You say you found it's an underdrive, but in your PM you also mention the output turning 1.25 turns for each turn of the input, which would be an overdrive.
The shift motor is a reversable DC motor that grounds through the case. Each of the 2 motor leads will make it run one or the other direction if connected to power. The earlier Doug Nash design used a mechanical limit switch inside the housing to control the motor. Power is applied continually to the appropriate case terminal, and the motor runs in that direction until the mechanical linkage moves enough to open the limit switch at which point the motor stops. Power can still be applied to the external terminal since the limit switch interrupts it. This design allows the use of a simple 2 position switch for control.
The later US Gear system eliminates this switch and instead uses an electronic timer to interrupt power after a set time. With this style there is no physical switch, and applying power to the gear box terminal would cause the motor to run continually and eventually burn up.
On most systems there is a mechanical limit system in the shifter leadscrew which allows the motor to continue to turn after the end of the travel is reached (ie it doesn't stall, rather continues to spin and the screw slips). On the older control system this doesn't matter because the switch cuts off power at the same time, but on the newer style it allows the motor to spin after full travel is reached if the electronic control doesn't cut power at the same time.
You could easily use a 2 position momentary switch for control, you'd just need to hold it down for ~2 seconds when you wanted to shift. Just wire each side of the momentary to one of the external box terminals and ground the case. The sensors on the case can then be wired to indicator lights to show what gear it's in. Of note, the motor loads a spring, so the indicator lights woln't shift until you unload the driveline and actually shift - there's no indication of the shift preload, so you don't have anything to tell you when to let off the momentary switch, you'll just have to count 1-2 seconds and trust it's ready to shift.
Automatic vs manual are generally the same except that there is some variation in input shaft designs. I think essentially all the Ford boxes are the same, the 2wd T-19 uses a special adapter shaft but the box is the same. GM & Chrsyler apps have some different shaft designs I think. The shifter electronics vary too, but this isn't a big deal. Manuals use a push/pull switch while auto uses a pushbutton in each case mounted on the shifter. Early control auto systems used a latching headlight relay, later design has the functionality as part of the blackbox controller. Early manual systems directly wired a push pull switch to the box, later ones use the same switch but run it through a different blackbox.