There are no parts inside of a stomp starter to engage the Bendix with the flywheel.
Just to clarify what you said Carl, the stomp starter engages the Bendix with a lever connected to the pedal (the same one that pushes the button on the starter switch.)
But you are correct, you can't just hook up a solenoid switch to a stomp starter and expect the Bendix to engage the starter.
Red, if you have the engine on a test stand, it's easy enough to push the lever on the stomp starter to start the engine.