I researched what kind of battery it was: CR2016, some kind of Lithium battery.

And boy, what a brain fart: I meant half a year, so six months. It's been a few years since I used that watch regularly, but I was impressed with the endurance of that little battery.

Skagen had these kinds of watches with their Hagen line. Ran on a standard battery for nearly half a month. You could set up notification groups so that the watch would buzz and the watch's hands point to a specific hour.