I am too, but I guess in my first quick read I thought he was not only starting his tractor, but running it too; seems he may have been only starting/stopping it to check charge. It's not completely clear from his first post, at least not to me, whether he's actually putting time on clock or just start, test charge at alternator, then shut off, come back sometime later and battery is dead? No criticism intended- just trying to get on same page with the OP and start at actual output to battery from alternator, not AT it.
Also try putting a load on the battery, headlights, with tractor running, and see what the output is back to the battery? Put the meter on the battery posts, NOT the alternator. Make sure all battery and negative cable connection at frame/chassis are clean and tight. If easily and safely accessible, move the negative cable near the battery while taking battery voltage readings, and see if it fluctuates. Same on plus cable. Then rev it up a little and see what it outputs to the battery. Report back results....
If you're reading volts, you have the meter on the wrong scale. To measure current draw, you need the meter set to a current scale such as 10 amps.
You're right. So to not confuse the OP further; volts is a measure of potential energy stored in the battery. Amps is a reading of flow of energy, OUT from the battery, (and in this case by a leak drawing the potential energy from the battery until there is not enough left to start the tractor).
If after running the tests I outlined above you can go back and hook up the VOM, (volt/ohm/meter on the lowest amps scale), and then retest between the positive battery post and the positive cable clamp, with the key OFF. If you get any amps reading note and report it back to us.
I try to refrain from counter posting unless it's to prevent harm,damage or injury. In this case it might be all three so here we go. Set amps to highest scale at first and if necessary reduce scale for precise reading. Test between negative battery post and the negative cable clamp to prevent short in case cable or meter probes come in contact with metal on tractor.