Slightly off track, but here are my A442F observations.
It uses a T/V cable to control line pressure also. Toyota refers to the 'extra' solenoid as a timing solenoid, and
after scoping it while driving it is active during shifting(also as Toyota documentation implies). I can't remember the waveform as it was four years ago that I did it.
All of the above is from before I pulled the gasser to do a 4BD swap four or so years ago, and my recollection fails me more and more...
I also ran the stock T/V cable to the IP for line pressure, and built a diode matrix to control the stock solenoids via the shifter, and added an extra switch for the torque converter lockup. The trans will lockup the converter in 2nd, 3rd and O/D. Will lockup at idle and easily kill the engine. 2nd or 3rd locked up, under load and would easily drag the engine to a stop.