When we talk about watches, let's not compare apples with oranges. The crafts which required a "standard" pocket watch were the engineers, comductors, firemen, trainmen, and track section foremen. In other words, those directly concerned with train movements. Dispatchers and operators of course worked with standard time, but they had standard clocks at their locations, and I don't know if they were required to carry a standard pocket watch or not. Maybe Rick can answer that question. There may have been a few other positions that required a standard watch, but I don't remember them if there were.
Employees required to carry a standard pocket watch had to have it marked up periodically, and it had to be at least a 21 jewel model with Montgomery (bold and black numbers) dial. When I hired out we had to have our waches marked up every six months by a certified watch inspector, those being listed in the employee timetables or special instructions. In earlier times when watches were not as dependable, they had to be marked up more frequently, even as often as every month. I carried my father's 23 jewel Hamilton 950B Railway Special, and I still maintain it in excellent running condition. Two years ago I had to have the main spring replaced, and it cost $300. I suspect that's about three or four times what the watch cost dad when he bought it new back in the 20's or 30's.
When a watch was marked up, the owner was required to carry a watch card while on duty, and we were often asked to see them by supervisors.
A lot of railroad men who were not required to carry standard watches carried pockets watches anyway, but these were often 17 or 19 jewels, and it was not necessary to have them "marked up".
When operators went on duty, or at least once a day where there were operators all three shifts, they had to compare their standard clocks with the standard clock in the dispatcher's office. Again, Rick can tell us more about how this was done. Then when crews went on duty, we would compare our pocket watches with the standard clocks at that location, or if we went on duty where there was no standard clock, the conductor would call the dispatcher to get the exact time, then the rest of the crew would compare our watches with his. If our pocket watches varied more than +/- 30 seconds from standard time in a 24 hour period, we had to take them in for servicing or repairs.
The first wrist watch that qualified to be marked up and used as a standard watch was the Ball Trainmaster self winding watch. I have one of those too, but I never used it as an engineer. The next wrist watch to be qualified was the Accutron battery operated. They may have been others after those, but I don't remember what they were.
The modern methods of dispatching trains have, as far as I know, rendered the use of standard clocks and watches pretty much redundant, but I can remember a time on the Monon when our lives depended on good pocket watches, and I've seen several times when I'd given about everything I owned for just one or two more minutes of running time. / Ron