That does seem to be doing almost the right things.. the three positions are being set.. its all just looks like its too far towards the firewall.. I would definitely lengthen the EDIC rod and see what happens - there's plenty of room for adjustment looking at the video. I'm pretty confident...
I'm unsure of the pinout on the connection to the EDIC motor so any tests without removing it are difficult to conceive of. If you do go to the effort of removing it then it's possible its the same circuit as for the 47 in which case.. this may be useful.. you're going to need to be pretty...
Something like this.. whilst Toyota called it a "Relay".. its got a Printed Circuit Board inside - corrosion often occurs.. I cant be sure where it mounts on the HJ45 specifically, you may have to hunt around for it. My best guess is still the passenger footwell though.
Yes.
And the EDIC currently has the Fuel Control Lever pulled back to the Overfuel position for START. These are the three lever positions the EDIC should use for correct operation.
You likely have an EDIC Motor or Fuel Control Relay fault.. you need to get your eyes on your EDIC Rod when you turn off the ignition - is it pushing the Fuel Control Lever on the injection pump FORWARD towards the radiator? If it is being pushed forward and the engine is still not shutting down...