Looking great, but regarding the electrical confusion, The Parts Book Is Your Friend!
If you'd checked there, you would have seen that the Series 1 interceptor takes a 6V battery, so it's a 6V system as stock. Some of the other ones you have read about have most likely been converted to 12V by their owners, and you could convert yours easily enough (fairly cheaply too, if your existing alternator is still in good shape). I can see where confusion could have arisen where the workshop manual shows both 6V and 12V systems, and the mid/late 1960's is when most British bikes electrics went from 6V to 12V. I don't know if any very late Series 1 models were shipped with 12V systems.
The LATER Interceptors (S1A and S2) were all 12V from the factory, they would have a zener diode voltage regulator (mounted on a finned alloy heat sink) as part of the 12V system in the days before combined reg/rectifiers. See items 44 and 36 in the parts book drawing (which also shows the points ignition which replaced the Series 1's magneto).
https://www.hitchcocksmotorcycles.com/partsbook-pages/3258Hope to see and hear this one running soon.
A.