That BOSE is a DVC sub huh? Interesting.
I apologize in advance if this response is not helpful.
My standard advice is to have someone more experienced do your install. Unfortunately it is very easy to fry things in stock radio wiring harnesses (and the expensive head unit) and it seems that you do not have a lot of experience with car electrical circuits in general based on your questions so far, but I could be wrong. You do know that you'll need to run fused power all the way from the battery directly to that new amp/sub right? Or were you planning on ripping out the Bose and using its power? Have you ever done this before? Why are you doing this at all if you don't know how to test a wiring harness for outputs? So many questions... never mind.
I could run you through testing voltages, currents, ohm'ing out lines, etc., but it would be easier (for both of us) for you to educate yourself on a car audio forum or youtube. There are lots of videos about installing subs, tracing wiring, etc. I am surprised your search didn't help you.
Installing a 3rd party amp/sub is easy. Doing it right to actually get more than a booming nightmare for a result is much harder.
Pay Mazda and get the wiring diagram. It will be worth it. You already paid ~40k right?
Otherwise use your meter to find any 12v power leads to avoid, then get a crappy speaker from an old PC and touch the leads to the harness with music playing on either the left or right channel until you hear/see an in-phase signal. Test that signal for level and polarity and off you go.