The Aussie has an inductive pick up for both sensors, in side the box.
It appears that the JDM has a Hall Effect sensor for the No.2, and an inductive pick up for No.1.
This is probably due to not being able to fit an inductive pick up in the front diff. The inductive has to rotate a magnet, with a winding beside it. The Hall Effect spins a shutter wheel, with the chip in the center of it.
The output is different, the inductive is a AC signal, of at least 1V p/p, the Hall is an 5V square wave. The outputs may be compatible, if the TCU uses a Smitt Trigger input, it would still register the pulses, regardless of one being zero crossing, and zero to 5V.
The other differences are,
A. that the Hall needs a 5V feed to it, that the Aussie does not.
B. that the output of the JDM/US is at road speed, so it can be a true speedo feed. The Aussie has the final drive ratios between it and the road, so it has to be divided by the final drive ratio before feeding the speedo.
As you suggest The White output wire could be feed to the speedo, but it also needs to go to the TCU so it can see the difference in front/rear speed sensor outputs, to operate the Limited slip clutch. Whether the TCU can just handle the two different signals, the No.2 at road speed and the No.1 at tail shaft speed, as base, and then look at variation to work the LSC, I don't know.
I suppose it would be a start to do this and see the effects, the other way would be to fit the Aussie No.2 inductive pick up to the JDM box, and leave every thing the same.
Harvey.