Yep, that would be correct. You came up with a pretty good summary. Detex was one of the main companies making them. You can see a history of them and some pictures of their clocks here
http://www.watchclocks.org/Types/Collection/history/history.html
Nowadays, they generally use wands and wall sensors to do it electronically, so the days of keyed watch clocks is at or near an end as companies phase them out for more modern methods.
As for the age, I would guess 1920-1950, but maybe someone here who is more of an expert on this topic can contribute more. I’ve seen your exact key before, but you know how it goes…when you look for something you can no longer find it. You can try searching “watch(man) clock keys” or “watch(man) clock history” instead of just “watchman key” for a more direct search if you want to learn more about them.
Without knowing your area and railroad, I’m not sure if it would have been used there or brought home and lost by someone. If there’s something that would have needed monitoring, then it’s certainly possible it was used there, but they were not used exclusively for railroads.
Hope that helps some, let me know if you have any other questions, and I’ll keep an eye out for your key still to help more with age.
