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There are a couple of records in which U.S. Navy navigators and quartermaster mates (QMs) could have recorded the serial numbers of the marine sextants they used for celestial navigation. One source could be what was called the star sight book (I found that in an old copy of All Hands magazine (https://www.navy.mil/ah_online/archpdf/ah196102.pdf ). Another source could be an equipage log or inventory that was maintained for all bridge equipment by the QMs (items such as binoculars, optical rangefinders, dead reckoning tracers, and so on).
Unfortunately the Navy considers such publications as temporary records. According to the Navy's SECNAVINST 5212.5C Change 5 (admittedly an older version, but it captures the Navy's historic treatment of these records), records that fall under Standard Subject Identification Code (SSIC) 3531 (Aids to Navigation Records) says this for "CHARTS, OCEANOGRAPHIC OFFICE PUBLICATIONS, NOTICE TO MARINERS, ETC., AT SHORE ACTIVITIES, ON BOARD SHIPS, AIRCRAFT SQUADRONS, AND OPERATIONAL STAFFS. Destroy when obsolete, superceded, or no longer needed for reference.
The notation under SSIC 9400 (Command Surveillance (Shipboard Installation) Records includes records pertaining specifically to "non-electrical and non-electronic navigation aids" states "Destroy when 10 years old."
I'm sorry we were not able to get you the information you were looking for. The only suggestion I can make to you is to contact maritime museums, especially the smaller local ones. They sometimes accession the memorabilia of local veterans, and sailors have been known to walk off ships with government property in tow... Perhaps an old QM left a boon with a local museum.
Thank you so much for taking the time to provide information and direction to my request!!!