It is very important that the alternator and regulator are grounded very well. I don't have access to your wiring diagram, but a lot of manufacturers run a wire that ties the reg and alt grounds together. It is so important because just a very small difference in voltage potential at the rotor (field windings) makes a large difference in the stator windings (alt output).
I don't know how far apart your alt & reg are, but if your voltmeter leads can reach from one to the other, try touching one lead to the reg case (near where it bolts to the tractor) and touch the other to the case of the alt (be sure both cases are VERY clean where you touch the leads). With the engine running, the voltmeter should read absolutely zero volts (not even a tenth of a volt) If your meter has different scales, be on the smallest scale. If you get any voltage reading at all, try using a wire in place of the voltmeter and see if it brings your charging voltage down to 13.5 to 14 volts. If it does, then check closely for bad/loose/corroded ground connections.
If the voltmeter in the above test shows zero volts, sorry, I am out of (realistic) ideas.
I suppose it could be an internal short in the alternator, but personally, I think that would be very unusual; I have never seen that, and can't visualize how that might happen. I think it would be more likely that the wire carrying voltage from the reg to the alt field is shorted to positive battery voltage somewhere (& the chances of that seem to me to be infinitesimally small)
If the alternator does have an internal short, you could remove the (probably two) small wire(s) at the alternator, and the charging voltage will remain high...I predict the alt will stop charging.
By the way...an alternator that doesn't charge will just drain your battery....one that over charges can do serious (expensive) damage.
Best of luck! Please let us know what you ultimately find.
