Looks like you're getting there. Is there no schematic available?
I've not found one. If anyone has any i'd appreciate it. The mower says 'XWL 2300 Quad Loop' on the front, and also 'Millennium edition XX of 100' . Makes us think it was a special run of mowers. Unfortunately, the manual section of dixie chopper doesn't list it, nor can I ever find a 'XWL' model mower, anywhere.
The closest to a diagram I found was just for Kohler model Dixie Choppers, but even then it didn't go into this detail. Just the switch level.
We've soldered a new diode inline, shrink wrapped the new connection and rewrapped the bundle. A few restarts and everything is behaving as expected! Time will tell if it solves it, but for now seems to be good.
Not rocket science to trace cables if you have a fault; but incase any other unfortunate soul stumbles on this. It's worth knowing there is a pair of diodes coming off the fuel solenoid which tie into the L and S side of the switch. The symptoms I initially had were 100% in line with a faulty switch, but to know these diodes existed within the engine harness offers another entirely plausible cause for the behaviour we had.