https://www.gaspares.com.au
Search engine is reasonably good try using ignition switch / starter switch. or just plain switch.
Most switches will be marked underneath
B = battery
S = Starter
G = Earth
M = magneto
A = Alternator
L = lights
There are only 4 mower switch makers and only about 8 switch variations.
The K & T web site you have been sent to before has the Briggs alternator replacement PDF on it and in the end of that is the basic wiring diagrams for almost every mower.