Check the electrical connections: at the battery, at the starter, at the frame grounding point, and at solonoid.
Check for corrosion, or for loose connections.
Also.. will your battery go dead after a while of just sitting in the tractor ( short ) ?
Try a load test. Either buy a cheap load tester, or run the tractor by your usual car mechanic and have it tested on the machine.... Or pull the alternator off and take it to a shop to be tested.
An inexpensive automotive cigarette lighter style load tester will be sufficient.. just alagator clip it up.. or install a cig lighter outlet like I did.. for aux power, etc.
A VOM can also be used but takes more time, and observance. Take a voltage reading before starting, watch the needle/display during start, and whatch while running, with no electrical devices on.... voltage shoul come up slightly above level it was when off before start. turn on your lights for a load... voltage could waver a second or so, reacting to the load... but should still read between 12.6 and 13.6.. up to 14.5 max.. or you have a problem in the charging system.
Run with a load for a while, then check the voltage again... if your charging system is week.. the voltage may start to slowly drop over time. Also check voltage at lower and higher engine rpm... significant voltage variance at different rpm also means a problem. ( Some voltage change will be okay.. .6 volt, etc... ).
Also.. check the voltage regulato connections.. especially it's ground reference... a bad ground reference will really shorten the life span of the regulator, and the alternator.
Chris / Soundguy