Since it seems to be unclear how these things are actually controlled, I'll see if I can explain it a bit:
Mechanically, the box is shifted the same was a manual trans is - there's a sliding collar that moves either forward or aft to engage the teeth on the gear and lock it to the output shaft. This collar is moved by a fork that rides on a support shaft riding in bushings in the case. Where this differs from a manual trans is that instead of a shifter that engages the fork and is moved by hand, it instead has a spring loaded lever assembly connected to the worm screw that is driven by a 12 volt motor. The spring allows the motor to preload the shift and then it rapidly shifts the collar once the drivetrain is unloaded. This is why you hit the control switch several seconds before unloading the drivetrain and actually shifting.
This motor is run off of 12 volts DC and is a reversible 3 wire type, with one "wire" being grounded through the case. Applying 12 volts to one of the other 2 wires causes the motor to run in a direction. That is, to run one way you power one wire, and to go the other you apply power to the other. These 2 wires are the 2 screw terminals on the flat face of the box.
There are also 2 contact switches on the shift rail on the rear of the box. These are solely for indication and have no bearing on the control or operation of the box. These are the 2 switches with 2 wire connectors molding into them. These sensors control the indicators on the automatic control box that indicate what range the box is in, and they are setup directly off the actual shift fork rail so they indicate what range the box is actually in, not what the control says (cause remember there's the spring linkage, so you can have selected hi range and had the motor run and preload the linkage but still have the box in lo range because it hasn't physically shifted yet.)
So, in order to shift gears what we need to do is apply power briefly to the appropriate motor lead. The worm linkage is designed to overrun at the end of it's travel so we don't need to be too precise on the time we run the motor as long as it's at least enough to complete the worm travel needed (~1 second), however excessive running will cause wear and potentially overheat the motor, so we don't want to do that.
The Doug Nash boxes solved this problem with a physical switch that was installed on the inside of the flat cover on the side of the box. This switch cut power to the motor as soon as the worm got to the end of it's travel. This is a very elegant and simple design but was prone to dirty contacts and breaking eventually. This same switch design was used for years on 2 speed rear ends however, so I'm not sure if it's really as unreliable in these as common knowledge says or if it's just normal wear for a 20 year old system that doesn't get used frequently.
With this style of motor switch, the in cab controls are very simple - just a push pull switch on the shifter - ie same setup used for a 2 speed rear. The switch in the box turns the motor off once it's done, so all you need to do is put power to whichever motor wire you are shifting.
The original automatic control is a bit more complicated because it's designed to have a pushbutton selector switch on the shifter similar the OD switch on an E4OD. However, it's still pretty easy as all you need to do is switch power one way or the other. The unit I have uses a Nissan headlight hi beam relay to control the motor power.
The US Gear box, however eliminates the in box control switch which in turn requires more complex control electronics as you need to incorporate a time delay. For a manual system, you still have the same push pull switch, but rather than direct connecting it, you need a system to cut the power off to the motor after 1-2 seconds. (1.6 I think was mentioned?). This is not that hard to do, but requires some custom electronics work to implement. Likewise, the auto system has the same problem, but with the added complexity of being controlled by a momentary pushbutton.
So, if we are trying to get a DNE style box to work, the wiring is very simple. Even for a automatic, if you don't mind having an actual switch rather than a push button it's pretty easy.
The USG is somewhat harder due to the time delay. However, it appears that the box could be reverted to the DNE style control merely by installing a limit switch on the inside of the cover plate, and this switch is readily available new for ~$15. Then just wire it directly up to a Eaton switch and go. If you want, the indicator switched on the back can easily be wired to a pair of indicator lights to tell you what gear you're in.
