Matthew, I'll jump in here with a few comments.
First, look at the starting circuit diagram that Chuck posted. Note that the TDC module is not a part of that circuit.
Also, if your tractor is a 1983 tractor with the original B48 engine, it is equipped with a Bendix drive starter. You talk about jumping some "solenoid" to get it started. On the Bendix setup, the solenoid that controls current to the starter motor is on the right side pedestal, under the battery. Just what did you jump from-to? If it was from the battery to the one terminal on the starter, you were bypassing everything. If your tractor has been retrofitted with the 1986-up P218 configuration, then you have a pinion-shift solenoid mounted piggy-back on the starter motor. What is your starter configuration?
To check out the starter circuit through the safety switches, turn PTO's off, transmission in neutral, and turn the ignition on. You should now have 12 volts on both of the transmission microswitch terminals. If not, check the voltage coming out of the 20A fuse; should be 12V.
No voltage at the fuse? Then back up with your voltage tests at points back to the circuit breaker (which is also under the battery).
Voltage at the fuse output but not at the neutral switch? Move forward testing the terminals on the front PTO switch, rear PTO switch, and in/put of the neutral switch. Voltage on one side of the switch but not the other means problem in the switch or its connector.
From the neutral switch, starter solenoid power goes to the ignition switch S2 terminal. The ignition switch closes the starting circuit to the solenoid from the S2 terminal when you turn it to the start position.
That's a quick summary of how the circuit works.
You need to walk through it with a voltmeter to find out where the 12 volt power is vanishing---that's your problem point.