Good luck with the project. My first ride was a '63 TR6, which was the first year for the "unit construction"......(which means the engine and trans are all one unit and not separate). First of all, for (electrics on a Triumph), you're talkin' LUCAS. Lucas electronics are infamous for problems of various sorts.
Mine had a battery and worked fairly well, a buddy had a '57 model with a (mag) and you didn't want to try and start it if there was any rain storm within 50 miles of where you were.........
It was my favorite bike ever. I'd get another one if I could find one at the right price.
From memory.......I can tell ya that a unit construction motor weighs 129 pounds and the stock rear sprocket had 46 teeth.......and my 60 tooth "overlay" sprocket made it pretty good for enduros and hill climbs.