As fate would have it, I just developed the same problem with my '76 Midget. Here's what I'm going to do...
1. Check the battery contacts.
2. Check the chassis ground strap.
3. Put a voltmeter between the generator and battery...If all is well, it should read zero volts. The lower voltage side (watch polarity) indicates the side with the problem. In other words, if the battery has less of a voltage than the generator, it's time for a new battery, if the generator has a lower voltage, that's where the problem is. It may be a loose belt, gummed up commutator or poor connections, but at least I'll have isolated the problem.
On their death bed, nobody ever said, "Gee I wish I'd spent more time at work!"
'68 Sprite 1275
'76 Midget 1500