Neither Eterna or Jaquet Droz produced huge quantities of watches compared to other makers....but but are respected for quality watches. Any decent watch maker should be able to service this piece, no need to send it to Eterna (unless you want to). Wouls need to see movement pictures and close up of all marking to give you any kind of real answers, the Eterna 3000 series was around early to mid-sixties, but other than that you are on your own. A watch of this vintage needs a service!
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Later, GaryRemember we are the caretakers of mechanical art.....
Member NAWCC, National Association of Watch & Clock Collectors