Ok a little update;
I've found that a 3-wire cable running through the engine bay is completely shagged, and I think this is the problem.
The other problem is, I don't know what's plugged in at the other end.
The top end of it is the bottom plug on the 3 vertically stacked plugs, in front of the large circular engine bay loom. The wire runs down and to the left, then comes back up and connects to something behind the oil filter. I can feel that it's connected into some sort of sensor, but I don't know what it is, and it seems to be hard-wired so I can't just pull it out and replace the wires!
Does anyone know which component this cable serves, and how hard it is to change?