I absolutely love Keymatics, but really they weren't very good machines.
They were unnecessarily complicated and quite unreliable.
The wash action is poor due to the tub tilting backwards when full and the extremely high water level, the clothes aren't so much lifted out of the water and dropped back in it, more sort of tumbled in deep water, which isn't as good an action. The wash time on standard cycles is only 4 minutes, though the machine tumbles during the heating phase too which helps. (I think they alternately tumble and heat, not both together?? It's been too long, I'm not certain of that.) I don't think the pulsator adds much to the wash, it's just below the water surface and much smaller diameter than the Hoovermatic twin tub pulsator. The one-way only tumbling doesn't help, either.
The very last versions in UK had a 4th rinse, there would be a reason for that... The Aussie ones were always 3 rinses, AFAIK we never got a 4th rinse version. Aussies are very water conscious. There was only one, 15 second intermediate spin, though the rinses were deep.
One good thing about them was the lack of vibration on spin - the cable suspended drum could shake about on spin, but it didn't transfer to the body of the washer. They were on wheels, so the excellent soft suspension was needed so they didn't wander.
The two pressure switches reflect the technology of the time - they were each single stage pressure switches. Later technology gave us two and three stage pressure switches, and later again, infinitely variable pressure sensors.
In the Keymatic, the low level pressure switch turned on the tumbling when the water reached the low level, but fill continued (may have a change of fill temperature, depending on the cycle) until the high level switch clicked over, which turned off the water and turned on the heater, if needed.
During Tumble phases the pulsator clutch solenoid is activated to prevent the pulsator turning, during the actual wash or rinse phase (in cycles that use the pulsator), the pulsator clutch releases, which allows the pulsator to turn - the solenoid is activated to prevent pusator action. The pulsator is only allowed to drive when the high level pressure switch is satisfied.
When pumping out, the timer does not advance to spin until the low level pressure switch has reset. (actually after pressure switch resets, it moves to distribute the load by tumbling for 15 seconds, then the timer advances to spin, where the main motor instantly reverses to spin the load.