How do I get the back off of a 1980s Armitron pocket watch?

I have my dad's 1980s Armitron pocket watch, the kind sold at places like Sears and K-Mart, but I can't figure out how to get the back off to get to the battery. I was able to move the back half a turn with a rubber grippy ball, but it wouldn't move more. I have tried using a thin watch tool but there is no notch for it to go into, and even the thinnest tool doesn't fit into the seam. Does it screw off or pop off? I even called Armitron to ask and the lady from some foreign country not only wouldn't answer but acted as though I were some kind of alien for even wanting to access the battery. All they would do is tell me to take it back to Sears. This thing isn't worth much -- it was a novelty "hunter's" watch that my dad kept for sentimental reasons -- and I don't want to pay anything to get the back off when I already have the tools. Can anyone help please?