OK, my petrol Lightweight has battery negative to RH wing, and chassis to starter-motor, and all contacts clean to bright metal.
I suspect the electrical connection wing-to-chassis is dodgy. I haven't seen a specific strap (it's not FFR) but should I be looking for one?
(Oh, and it might be the solenoid, but I'd rather not buy a new one until I'm sure of the earth side of the circuit.)