I do not have any experience with this type of system, but love a good electrical mystery. I do think the part you point out in your diagram is the pressure switch to the right in your picture of the setup.
The circuit board you are seeking will be "up here" (in red) in your diagram.
The black item on the circuit board I would suspect is a
transzorb for voltage spikes caused by the solenoid coil (and is located across the pressure switch contacts). The other beige item with one stripe I believe is just a "jumper".
As I said I have no knowledge of this system and your pics are not showing the complete set-up.
The transzorb