Still waiting on parts, but I made a little progress this afternoon. For safety reasons, new mowers have a brake that stops the flywheel when you stop the engine. For my application, I decided to remove it. Inside the brake mechanism is the kill switch. I cut the wire and ran it out of the cover to control it remotely.

Here is the brake/kill switch mechanism. A cable normally runs from this to a lever on the push handle.

Here it is put back together without the brake; you can see the wire coming out that will run to a remote switch or relay. This wire kills the ignition when it is grounded: