Sorry I didn't have time prior.
Continuity is used to test that whatever circuit you are working on, doesn't have any breaks in it...as in a broken wire, bad connector/connection, etc. Color of your probe doesn't matter what you touch to what...if you touch the two of them together, it will beep. You could use the continuity setting to check for ground. Hook one probe up to a known good ground on the truck (like a dash screw or threaded hole) and touch each of those "clips" in your picture with the other probe. When it beeps, you know which one is ground. If it doesn't beep, your ground to the body is probably the issue. You can test THAT ground by touching another spot on the body and making sure it beeps. You know you are grounded if that happens.
Once you establish which of the three is ground, then you should be able to switch the meter back over to DC, and using the same ground, probe the other two clips to see which is 12V with key in run.
Once you've got the +/- figured out, the final is continuity on the sender wire/clip. Take one probe, and using another wire that is long enough, connect it to the temp sender end of the wire. Then use the other probe, touch it to the clip that is not + or -. It should beep. If it does, every section of wire and connection between the two probes, is good...There are no breaks in the wire. You can THEN, when you take the probe off the engine bay side of the wire, ground that same probe (so one probe is connected to the cluster clip for instance, the other to ground), it does NOT beep. That means the wire jacket is intact, and the wire is not shorted to ground.
You can use a test light to check for + and - of course, but if the light is an LED (polarity specific, so will only light one way) it would be more useful in this case. You would only get the light to come on between the + and - with the key in run of course. But I don't want to muddy the waters, if you've got a multimeter now, then you should stick with that. The light is too limited/too much of a hassle for most things, IMO.