What grade plug are you using? I've had no end of problems using NGK B8HS, swapped to a 6 (hotter grade) and has been fine since. (I suppose this depends on what fuel and oil you use though, I'm in the UK and hence get 98 octane fuel. I do however, use cheap oil with no probs.)
As for the charging, if you're getting no charge then suspect dirty brushes/broken springs or burnt out resistor (the little coil on the genny body) If it's charging, just badly then it's most likely the regulator is out of adjustment. Probably advisable to swap to an electronic unit as per mztech's advice, link-:
http://www.mztech.fsnet.co.uk/index.htm All this assumes that you've cleaned all the connectors on the genny, battery and (most importantly) the block under the seat plus those on the regulator. If this has not been done then that's the first port of call, as standing for thirty years will have made sure that the 6volt electrics struggle to cope with the corrosion on the terminals.
Best of luck getting sorted, wish I was a bit closer & I'd have had a look myself. (Course you could always fly me out & put me up for a few days....
)
Welcome to the forum & to my abysmal sense of humour by the way!