Hello Bondy,
I see you have tested the resistance of your solenoids coil, you should have read some amount of value on your meter.
M on Key switch connects with Magneto wire from Honda Mower. (Correct)
G on key switch goes to Earth. (Correct)
B on key switch goes to Battery via Positive terminal on Honda Solenoid. (Correct)
L on key switch is not used as there are no lights. (Correct)
S on key switch goes to Honda Solenoid......Is it the same positive terminal the battery lead and B lead from key switch connects to? (No)
S on key switch goes to the black wire on the solenoids coil.
Then when you turn the key switch to start, at the key switch B & S are closed, +12V is then applied to your solenoids coil, energising it, you should here a click like Gadge said.
The click is the main contacts of your solenoid closing, sending power to the starter motor.
Very important bondy, ensure you are not creating any short circuit during this rewire.
Check/test all your wiring prior to connecting it to the battery.
Cheers
