Problematic to answer you properly.
The tech manual is dated April 1945, so these watches were in the ordnance system at that time. There is a mention that this case is a waterproof case that supercedes a previous version. It has a 987A movement. It is likely that it was originally issued before the start of WWII, but was updated then. I would suspect that a person would exchange his watch for a different one rather than wait for the watchmakers to service it and return it, much like any other piece of ordnance equipment. The "using arm" would only be authorized to perform certain small tasks, but anything more major, like watch servicing or replacing the barrel on a rifle, would be returned to ordnance for repair and a replacement issued. During a service, if there was a change to be applied, for example updating the case to waterproof, that would happen given availabllity of parts in stock.
This particular watch would have an OD stamped on the back followed by a serial number. "OD" represents a 17-jewel watch.
The actual technical manual is available as a scan on archive.org. I own a paper copy, and they are found from time to time on eBay.
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