Pull it and have a look at its guts.  Check the brushes and all electrical connections.  There's a "motoring test" you can do for generators to check certain things.  I don't know if that's described in the Jeep shop manual (I would hope so), but I know it's in my Ford Tractor manual.

I did work on the tractor's generator recently.  My problem was a broken wire going from the coil to the connection stud.  Easily seen when I opened it up, and easily fixed with solder (and Krazy glue to repair the bakelite bushing that was supposed to prevent the stud from rotating).

My tractor is the same year as my Willys (1949) and needs a lot more TLC to keep running.  Heck, if you stall the thing, you have to pull the spark plugs and clean them off with a propane torch before you can start it again.  That's not just mine--it's one of the first things people say on the tractor forum when someone asks about starting problems.   As for the Willys, in five years, I've never touched the plugs or points, and it starts every time.

-Paul

If it looks good don't forget to flash the the field.  The field coil's magnetism is sometimes lost due to shelf time or improper operation, among other reasons.


Best of Luck
Steve

It might be as simple as spraying the brushes with electrical contact cleaner while it is running. That is what I had to do to my '49.