You should only have to put the positive probe in the socket with the black/yellow wire, and the negative probe to some vehicle ground...but if you're getting a momentary voltage reading when you turn to and hold at Start, and it ceases when the key returns to On, then that might suffice, but I can't tell which wires you're probing in the pic to be sure.
But if you do get voltage, there on Start, that's good. We can rule out the ignition switch, and then work down the chain.
The Park/Neutral relay is in the engine bay, in the relay box on the passenger side. According to this pic below, it might be labeled as "N*P" next to the Fuel Pump relay:
Swapping the relay with a similar-colored relay is a valid test (as long as that component works, of course).
The final test is probing the black/pink line going to the starter. If all things check out and you don't have 12V on Start there, then time to trace that wire back to the NP relay. The starter is grounded to the engine, so all you have to do is ground your voltmeter on the chassis. Of course, the scary part of this test is that you'll be under the vehicle and someone will have to turn the key. I'd recommend disconnecting the starter wire and probing just the wire.
If you have power, then it might be your starter, though you noted you checked your starter already...how did you test that?