Sorted, I hope
I've spent the last two afternoons stripping everything down and testing. It turns out (I think) to have been a wire shorting on the headlamp mounting. All the wiring looked good, and with the headlamp cowl off the problem went away, but the clue was than when I put the cowl back, the problem returned. The wires come from below the headstock and up either side of the headlamp, where they rub against the metal of the headlamp mounting. There was clear signs of rubbing on both sides, although even after half an hour with a probe I couldn't find any bare wires. But I have wrapped the wires with a good protective layer of electrical tape, fitted everything back, and it seems to be fine. It looks like it must have been a tiny little short, although even now I don't know where.
It's been a good opportunity to check all the wiring and spray some ACF50 into all the connectors - and I have treated all the hidden bits of the frame while I was at it, so it wasn't a total waste of time.
Thanks to everyone for the advice and suggestions, and a prize to Vando for geting closest. Give the man a coconut.
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