My MD22L, which may have a similar setup, had a related problem. In my case the engine would not start.
The quick fix was to disconnect the wire to the solenoid and stop the engine by hand at the solenoid. Bought a new starter switch and it was not cheap being Volvo.
The problem was solved...for a while! Again I could not start the engine, and this time it was "very inconvenient",
but that is another story!
Pulled the starter switch out again and noticed that the problem was very intermittent. The cause was the multi wire connector just behind the switch, has about 15 wires from memory. One of the connectors inside the multi, was very tarnished and had become unserviceable. I made up a by-pass and all is well. And I now how have a spare starter switch.