many Generator engines will run with the battery disconnected. As stated by Cliff it’s probably worn out or short brushes. Changing them is not hard and for sure everything will need a good cleaning. Commutators can be cleaned with sand paper and high mica with the end of a saw blade cut off.
There are probably You Tube videos on doing it if never have done one. I started doing them as a teenager.
May be the right time to upgrade to an alternator if you’re not worried about originality.