i assume this is a single phase generator. (although i have seen some 3 phase generator when i was back in the military that were only 1k generator.) anyways. i would check to see the brushes in the coils are getting polarity contact. you could trace back accordingly.
it would be best if you can get a diagram schematic of the unit (if possible). however, if you don't you have one to look at then you're pretty much shit out of luck and have to guess what each circuit does and check to see where the electrical cut is at.
Back way when, i was working on 200k generators. their problems were always mechanical, something albiet easy to fix. i never really had an electrical issue so hard to fix that i couldn't find out or figure out what it would be. although i had schematics of each and every thing i could need to figure it out and the tools to test and to do so.
i would first see if the generator coil(s) have any output at all (with a durring operation testing). If they are bad then you paid too much money for the thing and just pull the motor and junk the rest. use the engine for whatever you like.
it would also do good to test the voltage regulator, (if bad you can replace that with an aftermarket one. (you can even use one from a car like the old 72 ford that had them on the chassis.) Test the Hard lines to the receptical. and so on and so on.
good luck