There should not be any electrical connection between the mower and the engine when you are doing diagnostics, Paul. I suggest you disconnect the kill wire at the coil and try the engine. Somewhere in the world there is a previous tenant who connects kill wires to plus 12 Volts, which plays hell with ignition modules until they suffer an early death. It is a regular source of disaster in our archives.
I wasn't thinking about the mower itself, and had not realised you were allowing it to be connected to the mower electrics. You should never do that when you are looking for a fault.