If this game is in the same universe as the White Russian game. According to lore, is the watch some demon artifact?
Ha! Somehow I didn't see this comment until now. I like the theory, and I think could maybe hold weight? Personally, I've always viewed the watch as only working so long as the character believe it works and not necessarily having magical powers beyond a basic placebo effect. First Leah believed the watch was working, then all her classmates did too. This is why other objects wouldn't work, as the characters didn't believe in it.