Hello. It sounds to me like one of 2 things is happening here. There could be others, but this is where I would suggest you start.
1. A relay is stuck.
2. There is a short in your key switch.
Both are easy to test/check. First of all you will need an assistant (I assume) to test the key switch. With the key off, take the small wire off the solenoid. Get a multi-meter and set on the lower voltage setting for DC current. Turn the key on (Where assistant comes into play), and check for 12v in the small wire you have just removed. There should be none at this time. Have the assistant turn the key to "Start" and watch for 12v at that time (this is where you should indeed have a voltage reading). If you have voltage at all times, you need to check the relay. Your machine probably has 2 or so relays, a small black plastic cube with 5 spade connectors coming out the back and plugs into a plastic connector. This diagram shows the wiring schemcatic. If one of these is sticking it will continuously give 12v to the solenoid, activating it and causing the starter to turn at all times. Occasionally, you can lightly tap the relays with a screwdriver and cause it to release. Either way, you will need to replace it as it will likely stick again in the near future at the most inopportune time, and cause this issue again.
1. A relay is stuck.
2. There is a short in your key switch.
Both are easy to test/check. First of all you will need an assistant (I assume) to test the key switch. With the key off, take the small wire off the solenoid. Get a multi-meter and set on the lower voltage setting for DC current. Turn the key on (Where assistant comes into play), and check for 12v in the small wire you have just removed. There should be none at this time. Have the assistant turn the key to "Start" and watch for 12v at that time (this is where you should indeed have a voltage reading). If you have voltage at all times, you need to check the relay. Your machine probably has 2 or so relays, a small black plastic cube with 5 spade connectors coming out the back and plugs into a plastic connector. This diagram shows the wiring schemcatic. If one of these is sticking it will continuously give 12v to the solenoid, activating it and causing the starter to turn at all times. Occasionally, you can lightly tap the relays with a screwdriver and cause it to release. Either way, you will need to replace it as it will likely stick again in the near future at the most inopportune time, and cause this issue again.