Welcome to the forum, Craig.
I suspect that you've got a starter relay wired to the "on" switch to the panel. Somehow a signal (voltage) is getting to the starter solenoid when you are in the "on" position. I'm also concerned that it may be running the starter continuously.
Go the the starter on that engine
and trace backwards. If need be, disconnect the heavy positive lead to the starter, turn on the panel, and see if you get a voltage with your multimeter. Trace that voltage back to the panel. You may find that the lead for starting is on the "on" pole of the "ignition" switch rather than on the "start" pole. You might also find that "on" is connected to the starter circuit farther down, perhaps even at the starter solenoid.
Welcome to the world of tracing DC circuits. It can be fun, and it can be frustrating.