Originally Posted by MOS95B
the easiest way to test continuity is with an Ohm-meter. Infinity when open, zero when closed. No power required.
...except for the little battery in the test meter...
Yes, you're unplugging the switch from the car, then testing the switch, so basically it doesn't matter whether the ignition is on or off since the switch is not in the car.
Also, I'm going to go out on a limb here and guess that when the switch closes those two contacts, the HUD processor switches to Metric mode. Therefore when you unplug the switch for testing, you should find that your HUD is now in MpH mode, and if you short the two wires together at the connector (i.e. as if you had plugged in the switch and pressed the button), you should find that the HUD comes up in Metric mode.
So after you've gotten all through the above, you'll know whether you have a bad switch or a bad circuit, and take it from there.