Today I disconnected the speedo cable at the gearbox, and found that, as I had guessed, the cable had broken. I can't quite tell why it broke, as it's not a clean break; in fact, it's pretty messy, and there was a great deal of sand-sized shavings underneath the cover.
I'm very curious as to why is broke. The original, 'high quality' Land Rover-made cable had broken at exactly the same place, and I attributed that to resistance at the speedometer end due to seized lubricant. But the speedometer has now been redone, and there should be no such resistance. From the 'spaghetti' of the cable winding wire, it almost looks as if it broke by being twisted in both directions, as if putting the vehicle into reverse put stress.
Could it be that because the odometer does not move backwards, when the vehicle moves backwards, the cable twists? Would not the designing engineers have compensated for this? I'm sure there's a reasonable answer, but I don't know what it is right now!
Below: The first view, as removed from the gearbox housing.
A gentle tug with the pliers and the cable remains came out.
A view of the cable shavings around the gearbox entrance.
View of a new replacement cable, as it should be.