Are you sure the battery is okay?
Can you try another for a quick test?
Had a battery that would only show a 13.5 volt and thought charge system was bad. Turned out 1 year old battery had bad cell or something. After replacing alternator parts and regulator/rectifier.
Voltage test at battery terminals (use DC scale) should show 12+ volts at idle and 13.5 to 14.5 at full throttle.
Your amp gauge could be bad. This test will help prove that as well.
Sorry no wire diagrams and I'm not a tractor guy, just standard charging issues no matter what type of machinery.
Here is how I look at these issues;
Alternator produces the voltage, some have everything built in and produce 12 - 14.5 volts dc. Others AC voltage that gets regulated and rectified down to 12-14.5 volts dc by regulators and rectifiers. Amp gauges report how you are doing. Battery use anything above 12 volts to regen itself, rest goes to whatever is running, like lights and radios etc.
Between these is the wires. Good clean connections with not shorts or breaks are a must.
Alternators, regulators, rectifiers, batteries, amp gauges and lastly wires all can go bad.
Given all that the system should work.
Easy, never!
Good luck.