Just one point to chip in, from one beginner to another. I had one watch that had a back like that, and no matter what I tried, I could NOT unscrew it.
Then I looked at it VERY closely - and it turned out to be a snap-back, that just happened to have the little divots that LOOKED like a screw back. I even have one of those "crab claw" back removers, as well as the Jaxa-style remover that you describe. The crab claw only grips into two opposite divots, but can exert better leverage. I stopped short of (1) scratching the watch back, and (2) adding to my already more than adequate vocabulary!
It was only after I twigged that it was, in fact, a snap back, after spotting the tiniest of little "ledges" on it, that I used a Bergeon knife back opener to pry it open and it popped off as easy as pie...!
Luckily, nobody was around, but I still felt like an idiot!
-- Pete, Brisbane ============