Quick reply...
I have a mechanical wrist watch myself. However, it ticks so quietly that VU meter doesn't seems to be able to separate it from the background noise: birds, automobiles, keyboards...
If you can get VU meter to hear only the watch, as it ticks, then you can write down a threshold command which would be performed during each tick. Something like logging precise - in milliseconds - time for each tick.
Best wishes.
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Per aspera ad astra...