Firstly, welcome to the Forum.
It is not an ES model.
no zener diode as far as I can see, but I do have a Yamaha 42x-a1 regulator/rectifier unit. I also have the original Lucas 3DS rectifier.
Is the rectifier actually connected - White/Green, Green/Yellow and Green/Black wires to the three 1/4"-wide spade terminals, Brown/Blue wire to the 3/8"-wide spade?
On an '81, the three Zener diodes are a strip, one connected to each of the wires between alternator and rectifier. If you follow the Black cable from where it emerges from the inner face of the primary chaincase to where the White/Green, Green/Yellow and Green/Black wires emerge from the Black insulation, are there three wires of each colour combo.? If so, one's from the alternator, one goes/went to the rectifier or goes to the Yam reg./rec. and the third goes/went to a Zener on the aforementioned strip.
I have electronic ignition,
I cannot see an ‘Ignition Amplifier’ or ‘Transducer’ - what do these look like
"Amplifier" is what Lucas called the 'electronics box' of their RITA electronic ignition. Enter "lucas rita ab11 amplifier" into your preferred internet search engine and look at the returned images; if your bike still has one, you should find it behind one of the sidepanels.
"Transducer" is what Lucas called the triggering unit of their RITA electronic ignition. If you look at the right-hand side of the engine, you should see a circular cover in to the top forward corner of the larger engine side cover. Enter "lucas 5pu" into your preferred internet search engine and, again, look at the returned images; if your bike still has a 5PU, you should find it behind that small circular cover.
There is no fuse at all.
The wiring seems to be all over the place so I’m thinking of re-wiring the whole bike
My preferred option even when the wiring hasn't been messed with; Lucas made some ill-considered changes to later wiring harnesses.
A basic rewire's easy to do if you can at least work methodically. What's your experience, what would you like to end up with, etc.?