Thanks to the help here the problem has a workaround which was first
suggested by BobF I believe, which was to lower the pressure switch set
points.

With that one change, the water pressure motor & pump has been turning on
and off automatically for 24 hours now, and while the motor must be turning
on and off as water is used I haven't caught it in the act more than once.

I'll try to do things around the yard that are near that motor to try to get
a good handle on timing how often and how long it runs & let people who
helped me know the results as a courtesy to them.

Thank you - your help was instrumental in diagnosing & working around the
problem which appears to be an aging water pump that can no longer reach the
previous high pressure set point which was apparently well over 52 psi.
--
(There is also a non-related minor problem of the pressure switch pump
baffling gunked up which isn't the proximate cause of this problem.)