Hmm.
I think you need the regulator connected to the battery/alternator for the output of the alternator to be regulated.
Obviously 36 volts is the wrong answer: it should be 14 ish DC, but if it measures on AC, then I'd say the diodes are likely fried, but I can't be sure. The thing is, a short circuit on the output (the big wire) could have caused the diodes to fry.
My guess is a bad diode (or two) in the alternator.
While the function of regulators is very similar, I suspect you want to replace a regulator with the same one. I guess if I were on a desert island, I'd try whatever regulator I found,. but I wouldn't do this on my tractor. Unregulated alternators can put out very high voltages which will promptly fry the electronics, lights, etc., on a tractor or car.
Honestly, I'm flying blind here, and I'm worried you are going to damage your tractor. If at all possible, I'd bring it to a dealer or a mechanic.
Failing that, most cities have places which will rebuild alternators for a reasonable cost. I would get a regulator 'just in case'
You might feel better if you check out this site:
http://members.1stconnect.com/anozira/SiteTops/energy/Alternator/alternator.htm . It explains some stuff pretty well.
Good luck