that "plug" dont matter, it is just a metal conductor. Clean off some of the insulation to expose some wires in that meter lead. Now what you have there will work for this test.
Turn the meter dial to the lowest Ohms setting and touch the "plug" to the bare wires (black to red) The dislay should go from 0 to .003 or something... Pull them away and it goes back to 0

That is all you need to test the switch. Now test it in your hand, then put it all back together and find a connector down stream and test again...

I have not had to deal with this yet, so I cant say where those connectors are. the manual should have something but I aint fount it