With out the wiring diagram I can only guess what you have.  All mowers are wired different   I will say the starter ignition switch has 5 wires going to it.    One should be marked B, this one should have a positive power wire going to it.   Maybe one is marked G  and this one should go to a negative wire going to it.    The one marked s to the small starter solenoid terminal.   The one marked I to the coil primary wire.  They may have your ignition switch marked different which I don't know without a wiring diagram.   The manufactures change wiring from model to model and year to year???   Don't know if this helps or not.