Zener diode

Should be on the inside of the right hand alloy Z plate the footrest is bolted to.

https://andover-norton.co.uk/en/shop-drawing/223/support-plates-riders-footpegs-rear-brake-pedal-and-linkage

The facts above re the zener diode is about right. and the British motor cycle charging is poor BUT converting to the modern reg/rect will not get you more power. The reg/rect will stabilise the voltage better. And of course the Zener system has been with us 50. yrs, so not a bad record. Get the Zener voltage checked and it should be good. If out of spec (14.7V) Then move on.

I have sold rectifiers for over 40 years sold and tested Zeners and sold regulator/rectifiers for nearly as long. My opinion is that the zener has been more reliable than the modern reg/rect. The reg/rect has many components inside all subject to possible failure, And the design criteria sometime needs consideration.  I say again if your Zener checks out as ok keep with it.

Alan Osborn is correct; there is nothing wrong with a known zener diode.  My set-up on my 1978 Mk.III Commando is now around 45 years old and it is still working perfectly.  Likewise, my Boyer system, fitted in 1982, still functions well.  My machine starts third or sometimes second kick from cold and charges correctly.  Some faults with zener diodes were identified as owners incorrectly tightening them; the book says 24 inch pounds for the fixings - that's two foot pounds.

14 commando all with zener. If respected thermally, they will last longer than a human life.

Electronics, with capacitors, are not so blessed.

New podtronics still in box on shelf  after 30 years. One day, when I feel wild and reckless, I'll try one.