Dave K2, Terry B, Wes H, Keith E;
Nice job on interpreting and explaining the starting and ignition circuits.
Great addition to the schematic with the troubleshooting guide. Only "fix" is that the light blue wire is between your red "K" and "I," which is the generator "A" terminal and the regulator "Gen" terminal.
Zach;
Nobody here is trying to give you a hard time yet. You've listed your occupation as student, so I guess we're assuming that you're a person who studies. People will help, but you have to try to help yourself, too, sometimes more than once.
You said you have gotten it to both click and turn, so you're making headway. Congratulate yourself on that accomplishment, and have some patience. You know that one part of the system works, so you can move on to others. The more parts there are, the more chance of things getting out of whack. You need to get them back in whack.
I have located a fairly forgiving section of my garage wall, so that when I feel the need to bang my head on something, I don't do too much damage to myself.
As mentioned here before, some replacement regulators have a different physical appearance, so look at the terminal markings rather than the location of the terminals. The 12 volt figure is, of course, assuming that your battery voltage is measured first and has 12 volts to start with. If not, charge it and use the full measured voltage to compare at all the indicated locations in the chart.
Wes' comments about the battery terminals and ground terminals are also perfect. ALL the grounds need good connections, or something isn't going to work.
The comments about ignition points and contacts in the solenoid also infer that the points in the regulator should be in good condition and adjusted properly, but that has more to do with the charging circuit. By the time you have the tractor going, you'll be familiar enough with these processes that reading the manual, then cleaning and adjusting those points will be pretty simple. If there's been corrosion or other bad connections so far, I would kind of suspect the charging system to have some of the same.
Sometimes aggravation is a lot cheaper than tuition, sometimes not.