In my understanding, most NASA-issued watches were retained by NASA and ultimately transferred to the Smithsonian/NASM in 1977 (with the exception of Armstrongs's A11 145.012 in 1973 and Collins' A11 145.012 in 1990). Why the 105.003 was kept by Cernan after Gemini 9 is unclear to me but it is among the few listed as “On Loan to Omega Museum” here:
https://www.worldoftime.de/data/cms_data/files/6887018b54652924432c4e168ae869a3.pdf
Specifically your AJTT page says on loan from Cernan vs. other "On Loan to Omega Museum" watches that can be found in the Smithsonian's holdings. Perhaps someone else can clarify if NASA uniquely gave the 105.003 to Cernan or otherwise explain the outlier (looking at you @@TLIGuy!)
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