tubebender — Thanks for the links. They did lead me to the (quite thorough) installation manual. A repair manual may simply not exist.
All — I plowed on in anyway: Removing a cover on the compartment on the top of the pump revealed the start capacitor and a 115 / 230 volt switch. I was able to steal two capacitors from another project to get the right capacitance value and a slightly higher voltage rating. That starts and runs the pump. However, the old capacitor does so too: I’m guessing it “healed” well enough for light, temporary use. It shows no outward sign of damage — no leakage, bulges, etc., and the capacitance value is only about 5% low. Internal resistance is low too. If this is a capacitor problem, it is one that only shows up at high voltages and under duress — temperature sensitive, perhaps.
Of note is that since the pump has a 230 volt (AC) operation option, the original capacitor is rated at a healthy 350v AC. That should be quite the overkill on 115 volts AC, making for, I would have hoped, a quite long lived capacitor, for an electrolytic cap. (Maybe it has been - somewhere I was reading that to obtain a low failure rate of start capacitors, they should be swapped out every 3 years? Golly! Maybe that’s with typical Chinese production?)
The substitute cap pair won’t fit in the compartment that held the original cap. At present, I guess I’ll “rig” a little better mount and see if the pump works correctly for a few days. If it does, I’ll assume the old cap really does have a problem, and make up something more permanent.* If it goes out again, then the old cap is not the problem.
*I’ll also probably add an on hand 30 amp 480 volt mercury switch for the high current switching, triggered by the existing pressure switch. Plus I’ll add arc suppression to the pressure switch if any sparking remains. Can you say “overkill”? That should make the pump motor power switching last longer than I do! And the next owner of this place too.