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Murphy of course invoked his famous law at a time of considerable inconvenience when a collection of commitments could be disrupted in one fell swoop - although happily this could have been a lot worse. Nevertheless, I have had a little time to do a bit of experimenting of sorts. My post was aimed at trying to elicit helpful suggestions in a hurry. For those who might wonder how this story develops I can now add a small update.
The mystery remains: With a freshly charged battery installed it starts instantly (very frisky turn of the starter and the engine "takes") and then just as quickly dies. "This is promising" you are inclined to think so you turn the key again to restart, hopefully properly this time. No, the starter won't even turn although it attempts to. I have done this with two separate batteries, both of which I know to be good, and before that I had a jump lead opportunity (stone dead after the initial tiny wrooom, thereafter no improvement with the leads still on and the other vehicle running whereas it should recover within minutes). You can imagine my puzzlement and also how nothing discussed so far appears to suggest/explain what the ailment can be. Something appears to be acting like a short circuit. To me the alternator and/or the starter are prime suspects, but in any case this is an electrical issue.
I am grateful for responses here all of which I know are well meant, although I choose to ignore those replies which are laden with social media syndrome.