The starter is only going to spin if it has power going to it, that power is controlled by the solenoid.
The starter solenoid is just an electrically controlled switch. It allows you to turn on or off a larger gauge wire, your battery cable to the starter, with a smaller gauge wire, the wires that run to your handle bar switch. Disconnect all the wires from your solenoid and measure continuity between the larger post, the ones the battery cable and wire to the starter use. If you have continuity then the solenoid is bad. If it measures open, like it should, then short the two wires that go to the switch and see if it closes. If it does then your solenoid is good. Then measure continuity on the wires coming from the switch. It should only show continuity when you push the starter button. If it shows continuity without pushing the starter button you have a short somewhere in the starter switch or its wires.