That's one way, and it also tells you where due South is too. The watch is only one piece of information, solar noon changes from day to day (called the "Equation of Time"), so you need a way to correlate the two. An almanac would have that info, or the equation could be memorized and computed.

This isn't just recreational fun, most (maybe all) Navys still require having people on board each major ship that can perform sight reductions and wind up watches. The assumption would be that during a war GPS and electronic devices would be destroyed. The "stick in the ground" method doesn't work if you're moving, and takes a while, and speed matters when you're being hunted.

solar noon is the time @ the shortest shadow. You don't need an almanac for that. It's got problems, but if you're lost on land with a digital watch and a stick it'll work pretty well.

Just seeing the shortest shadow doesn't tell you anything. You need a way to correlate it to your position on Earth. Having a watch (set to a known time zone) only tells you what time it happened, which is also pretty useless. You need an almanac (or some computation) to correlate what time solar noon happened on a given day with your longitude.

Lost my last account's login. I'd watch this, you only need to know solar noon in Greenwich and compare it to your own solar noon.

https://www.youtube.com/watch?v=b7yoXhbOQ3Y