I think you're all right about the bad connection. On Sunday I thought that I'd cured the problem by tightening the starter motor cable post as it seemed a little loose. I assumed that the heat from the engine had worked it free. But when I hit the same problem a few hours later it was fiddling with the positive terminal on the battery that did the trick.
My battery posts, rather than the soft lead ones you get on normal batteries are solid brass screw in ones that taper slightly. As far as I can tell the clamps on the cables are not tapered so I'm wondering if this is enough for them to work loose. If you test the voltage near the battery but not on the terminals it still reads 12.8V but maybe the surge of power for the starter is enough to dislodge it. You can slowly turn the clamps on the posts which doesn't bode well. I may screw the B+ cable direct to the battery using a ring terminal rather a clamp and see if that improves things.
I'm really hoping that the loose connection is not on the terminals under the scuttle as that will mean an annoying amount of dismantling. I'm starting to regret burying so much of the electrics in inaccessible places.
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