Thanks for the help, guys. I actually get most of the battery stuff because we live off-grid -- we have a large solar array, battery bank, etc. Checking the charge and maintaining batteries is something I do frequently... well.. clearly not frequently enough for the tractor.
OK so more news, not the greatest. The tractor died twice on the road and bringing a battery the battery back and forth after giving it a couple hour charge enabled the tractor to run for 20 to 30 minutes. This clearly seems like a battery that is near dead to begin with, drawn down, and a faulty alternator. While the tractor was running I measured the battery at 12.60 (fresh after pulling off of the charger, tractor running) and only about 12.4 at the alternator. I will research replacing the alternator.
In other news I found out why the battery was dying so quick on the tractor -- the starter is getting stuck and running while the tractor is on. At first I thought it was my start button (aftermarket, not OEM Ford) so I pulled the wires off and that seemed to get it to try and start without having a run away starter but the battery was already near dead by this point. Later when I charged the battery again I tried starting *with the wires* and not the push button and the starter still kept on running after I stopped touching the wire ends. A local guy came over and felt sorry for me -- he recommended a place nearby that will rebuild the starter. Am I correct in thinking it has to be the starter and not the solenoid?
Thanks for all of the help guys. This thing would be dead on the side of the road without your help.