Hi Henry, a few more points.
If you do not have a wiring diagram, then get one.
I had no space in the previous post to add a comment on the fact that a "kit" was available from Triumph and also Lucas to replace the battery with a large value capacitor mounted on a spring (to protect it from vibration), which was supplied as a standard fitting on some "competition" models. The intention (I think) was to save weight.
To the best of my knowledge, most of these models were also fitted with lights, so I would think that this suggests that, in good condition, the charging system was capable enough to do the job (though only just, I think).
By the way, if your machine is not fitted with a zener diode, only 1 set of alternator coils is used for daylight operation with the rest being switched in when the lights are turned on.
All of the information I have given in both posts has not been recently researched by me, but is from memory and experience. There may be some inaccuracies but I am confident that the info is generally correct.
All the best with your bike and, as is often said as a parting shot among bikers in my part of the world, keep between the hedges.
Best regards,
A.
Twolitre - Your'e about the same age as me then?