Curiously, what function does it serve in that the mower will run with it bypassed?
When you read the stuff below, it's important to remember that there is a distinction between preventing ignition and shutting the engine down.
The ECM does only three things.
1. Checks the safety switches and prevents the mower from starting if it doesn't like what it sees.
2. Shuts the mower off if you get off the seat AND the PTO is engaged.
3. Allows you to shut the mower off with the key.
The safety-switch ignition check can be bypassed with one jumper. I figured this out and did it. The system can be rigged so the safety switches work to prevent ignition, but that takes more jumpers.
Ordinarily, I hate seat switches, but this one is actually okay, because it will not shut the mower off unless the blades are turning. The mower has a seatbelt, however, so the likelihood of falling in front of the blades is extremely low. At least it should be. My seatbelt latch is screwed up, so until I fix it, my strategy is to hold on tight. I have not tried to restore the seat shutoff function yet, but I may do it later.
I have come up with a cheap circuit to shut the mower off with the key. I have the parts, but I haven't done the breadboarding, testing, and assembly. It works in simulation.