I think the Peter Heinlein story has pretty much been disproven. It has been a while since I did much Horology, and my references are in storage. The latest I recall was that watches came out of Flanders in the late 15th century. Possibly originating in Italy.
The German lands were on the trade routs, so they quickly became the distribution center.

Having been personally to places like Basil and Nuremberg, this makes sense to me. These are still crossroad cities which even now still effect the transfer of information.

My impression from what study I did in reading some 50 years worth of Horological Journals is that by the mid 16th, having a watch would be like having a laptop in the early 1990s. When laptops were around 5 to 8 thousand dollars and were more of a luggable machine.

If a digression can be tolerated, regarding trade and information flow. When I went to Venice in 1998 some of the dolomite pathways along the canals were torn up for the installation of optical backbone. It was explained that Venetian warehouses, made for perfect places to locate server farms.

Looks like its a jerkin worn over a doublet.