Matt: I'm not sure you've clarified the issue for me. I'll bet if you go out to a tractor that has what MTD calls a "Battery" switch (as opposed to an "Ignition" switch), that is, a key switch designed to operate a coil powered ignition instead of a magneto fired ignition; and you switch the "Gen/Alt" terminal with the "Ignition" terminal you will see the symptoms similar to what I experienced for two years. Namely, the engine will "run" fine, but it will refuse to start.
For clarity, and in the spirit of Hydro Harry, the particular configuration I was trying to operate was a CCC 782 with chassis wiring for a coil-fired ignition mated to a magneto-fired engine (actually two of them installed one after the other). I used an interposing relay to convert the positive voltage originally destined for the (+) side of the coil into a "kill" contact for the magneto (through the N/C contact of the relay). The motor ran fine with the key in either the "Run" position, or the "Run w/Lights" position, and with the relay in the circuit, the motor shut off with the key. The problem was that relay refused to energize with the key in the "Start" position. I wound up rigging an ON-OFF-ON switch to energize the relay directly from the battery (thus disabling the "kill" contact to the magneto) just so I could start the tractor. With the tractor started, and the key in the "Run" position, I could manipulate the switch again to bring the interlocks into play and allow the tractor to be turned off with the key, or simply kill the motor with the auxiliary switch. It was a awkward solution, but I couldn't figure out why the motor wouldn't start with the key until the light bulb went off and I realized that I simply needed to put the "Ignition" contact at the key in the circuit when I started the tractor, not the "Gen/Alt" contact as the plug was currently wired. Once I switched the wires, everything worked as intended.
Note: Once the motor was rotating, it provided "Ignition" voltage for the whole tractor through the "Gen/Alt" contact, that is, "back feeding" the Ignition circuit through the N/O seat switch contact.
My motivation for all this trouble was to arm what I called the "safety circuit" so that the motor shut off if the operator tried to get off the tractor with the electric PTO engaged: which it did with the key in the "Run" position and the relay in the circuit. Paradoxically, without the seat switch in the circuit, the tractor started, ran, and stopped just fine with the switch wired up incorrectly!
I've written the whole story up with pictures and wiring diagrams, but the account ran to 40 pages, so I've been trying to edit it before posting it to my "Unconfugilating a 782 SN 714899" thread. I'm discovering that it is not hard for me to be wordy, but it is difficult to be wordy AND CLEAR. Harry has a real gift for it.