If have a voltmeter and ohmmeter WE can probably get you to connect your wires to the right places.
When OFF the M (coil kill wire ) terminal is connected to G. When the key is in any other position such as run start, etc, the M terminal and the coil kill wire is open to all other terminals.
When key is switched to on the M terminal is ungrounded and the B terminal MIGHT make to the Light terminal. (some switches have a extra position just for the lights only which is first on position.
When turned to the spring loaded crank, the B terminal to the Start terminal which applies 12V positive goes towards the starter solenoid little terminal.
Normally for 4 wires Red =B, Black = M coil kill, Start (can be any color sometimes white, and Green to G=ground.
Your coil kill wire is being connected to the wrong terminal of your ign switch.. If the coil kill wire only has 12v when key is in start it is connected to the S terminal instead of the M terminal of the switch.
What are your wire colors?
What is the exact Model number and name, like Gateway, MTD, or ???? (maybe we can find a 4 wire wiring diagram) if we had a name and model from your units tag on the chassis, not the model number from your owners manual.
PM chzuck is a good idea, send him the exact numbers off your machine chassis. I think he even has a tiller service and maybe a website. listed at his public profile. He has helped me get through the mechanical of the old Horse tillers and finding Service manuals online.
Do you have a voltmeter and ohmmeter?