I would say the starter solenoid is jammed/sticking closed, battery and starter solenoids are right side of engine on the firewall just inboard of the battery.
The ignition switch provides a small current to the starter solenoid that closes and allows power to the starter and cranks the engine.
Rotation of the key from OFF to L to R to Both de-grounds the mags making them live and allows a spark to the plugs, next turn closes the solenoid and energises the starter motor that throws the bendix into the starter ring and turns the engine over, releasing the key it springs back to Both position isolating power to the starter which allows the rotating starter ring to throw the bendix out but continues to de-ground both mags, i.e it keeps them live. (Some countries have a starter warning light, UK as an example, to show there is current flow if the starter solenoid sticks in)
What is happening is the starter solenoid is sticking every now and then as it is failing, when power is applied because the solenoid is closed, power is supplied to the starter and it cranks. This can be dangerous because if you start the engine and the solenoid sticks closed you will continuously throw the starter in with the engine turning it as well and this can cause a fire. Hence the UK has a light to warn you it is still connected.
starter warning light
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