In my experience with an older Onan your symptoms were same as what I had. It was the rectifier. I was told that the easiest way to kill one is a weak ground connection. The very nature of it just being mounted to the tin which is its ground is likely. Once I replaced mine the problem was solved.
If you replace it make sure the mounting surface will ground well.
You can check for battery drain. Disconnect one wire from your battery, then put a light of some sort in series. One end to the battery the other to the battery wire. If the bulb is lit then you have a drain. To find it you have to disconnect items until the light goes out. On these simple tractors it should not light at all as far as I know.
All this being said I have yet to see if I even have one on my 89 Onan. I can claim an excuse though. I have only owned it a day. So far I installed a 2" receiver hitch, fixed weak spark/poor running by snipping the ends off the spark plug wires and pinching the plug connecter slightly, while on a ride bypassed an inline fuse holder that blew a fuse to starter, adjusted the throtle cable to actually reach full throttle, then oiled it, removed tin next to starter so I could cox the starter to engage the flywheel, and then oiled same once home.
All this was because I promised the kids a wagon ride with the, new to me, tractor. Oh after all this I ran into the house when I tried to turn where there was sand with the trailer connected and my beer in my left hand. The hell if I was going to let go of my beer just to stop the tractor. Side note I got it without functional brake. Part did come today though to fix it.
I do believe I digresed and where is the spell checker? I am math and logic minded and not a speller.
Steve.