@JohnStahley Welcome to the Club! The P500 is a pretty straightforward machine, the intake temp sensor would be the only thing near the air box with wires coming out of it, just like the O2 sensor in the exhaust. Look back behind the head you may be able to see it with the seats removed on drivers side, if not may have to remove rear rack to get to it from behind or above.
Here is the parts fiche section it is part #17 in the diagram in the below link:
If ur looking in your air box its in the back left ait mod is only usefull if u live in a hot 80+ constantly temps well ( most will say) but you can add like a 5kohm resister usually 3.3k give or take is perfect to the power wire should reduce the temps to the ecu around 10 degrees or so that way if its 80s 90s the ecu wont pull any timing but remember doing this you need to run higher octane gas
Typically on fuel injection if you tell it the air coming into the air cleaner is colder it will add more fuel because the air is denser this is how we used to get the ping out of the Kawasaki nomads. By the way this play collects more fuel if somebody can come up with the right size resistor it would make a great post
Take the sensor out put it in the house of 80 degrees measure the resistance. Then put it in the freezer when it gets down to 50 degrees measure the resistance again that's what you need for a resistor. If the resistance goes up it would an inline the resistance goes down you put it across the wires