Its a 4 pin unit. Pin 1 is night time illumination, corresponds to a baby blue wire with red stripe on most Fords, not 100% sure on your 2013. Pin 4 is ground. Between the two are for signal. If your night time illumination works then there is no need to test continuity.
Next to illumination is signal return. Next to that is switch signal.
Each of the three buttons pressed (should) return a different resistance when measured across these center two pins. Not sure what those values are, but for example, RESET might be 500 ohms, INFO 300 ohms, SETUP 150 ohms. If you get absolutely nothing then the switch is bad and the numbers are moot anyway.
So if you have a meter and want to mess with it, set for 10K and put your leads on the two center pins and push any of the three buttons to see if they each have a unique resistance. If so, the switch works and trouble could be elsewhere. Assuming the unknown resistance value is what the truck expects.
For what its worth, the part number is 6E5Z10D889AA and is the same exact part used in 06-12 Ford Fusion, its Mercury and Lincoln siblings, as well as 07-17 Expeditions. So inexpensive and plentiful. Should be able to buy a new one for $30 something, obviously less for used. Furthermore, the same switch is used in a plethora of other Ford/Linc/Merc vehicles, just with a different colored/sized faceplate. The switch itself is the same.
