I think it all makes sense, Paul. Essentially, I think you had two problems in succession.
First, in the long ago, you acquired the engine with a worn-out decompressor pin. In the first part of this thread, that was replaced and the decompressor then worked.
Second, while testing the decompressor, you fitted the engine to a different ride-on which had a mysteriously malfunctioning engine. You hoped that, because the Tecumseh was running by then with its new decompressor pin, it could be a suitable engine for this second ride-on, which had a chonda copy of the Honda GXV390 engine in good condition except for a malfunctioning ignition module. The Tecumseh soon malfunctioned on that second ride-on, and you resolved the problem by disconnecting the ignition kill wire. Meanwhile the chonda engine worked perfectly once it was removed from that mower. So, it seemed highly probable that the second ride-on had tenant-improved wiring which may have been doing something like applying 12 Volts to the kill wire. With its kill wire disconnected, the Tecumseh engine worked well for a short time, then malfunctioned. The malfunction was somewhat erratic and intermittent, which made diagnosis difficult. Ultimately, having established that nothing else was wrong, you tested the spark while the engine was running. It turned out that the spark quality was changing when the the engine malfunctioned, suggesting that the ignition module had been permanently damaged by its time with the tenant-improved kill wire connected. So, you tried another ignition module, and the engine then operated correctly, supporting the theory that the original module had become damaged.
This has been one of our longest threads ever, and I think easily the longest thread ever that was solely concerned with fault diagnosis. Just in case there is yet another unexpected twist or turn in the case study, I'll leave this thread open. Since it will be open I suggest that you use it to trace the actual wiring fault in the ride-on mower. If you give us a full identification of the mower, we can try to get hold of a wiring diagram, and start making some tests.
