First of all I would ONLY have connected the old BAT wire to the alternators output stud as it wires to the ammeter (if it had one) or the hot ungrounded battery post eventually, often where the big battery cable wires to a starter switch or solenoid. The alternators output has to get to the battery somewhere even if via an ammeter if it had one to charge it.
2) I would not use the old ARM wire whatsoever as it used to attach to the gennys ARM post.
3) I would have upgraded the wire from alternators output to battery or ammeter with at least 10 or even 8 gauge.
4) If it had an old idiot light on a genny and Voltage Regulator system it wired from BAT on VR over to GEN/ARM on VR. If it was a 3 wire alternator I would have re wired it into the excitation circuit but if its only a one wire alternator I wouldn't leave it as you have it (but alternator still has to wire to battery remember) as it may be wrong BUT I CANY SAY NOT BEING THERE. To be safe for now disconnect it until you know how to wire it right as if its for the old genny and VR it may be wrong and the one wire alternator should NOT need external excitation wiring.
Basically with a one wire alternator it needs the correct and a good frame ground of course (usually NEG ground unless its a special, IS YOUR BATTERY NEG GROUND??????), then all it does is its output gets to the battery and it charges it. If its working check battery voltage tractor not running and if charged it is around 12.6 volts. Then start her up and once enough RPM is reached so it self excites, battery voltage should rise to al least 13 and up to 14 + subject to RPM and battery state and alternator and its voltage regulation circuitry.
If a one wire doesn't get enough RPM it doesn't excite so you need the right pulleys and RPM and a good tight belt and its output wired to the battery THEN AT SUFFICIENT RPM IT SHOULD PUMP AMPS INTO THE BATTERY AND ITS VOLTAGE WILL RISE
HOPE YOU HAVE CORRECT GROUND
Many auto shops will bench test an alternator for free, have that done ASAP,,,,,,insure ground,,,,,,,,,wire output to battery or ammeter, ,,,,,,,,,,,,,check battery voltage not running (12.6) ,,,,,,,,,,,,,start her up and at enough RPM it should engage and raise battery voltage (13 to 14+)
John T