As noted, I contacted grandson Neill Thompson through Thomas Foster's Ancestry.com genealogy documentation: 

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"I never knew my maternal grandfather, he died just a few months before I was born, in 1956. But I do know about him, and your research is spot on. Well done! You may find that the Foster genealogy is fairly well established. It is possible that my grandmother disposed of [his Hamilton watch] around the time of his death or any of several (now all deceased) family members of the next generation could have let such things go years, or decades later."

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"I have to tell you that I think there is some contention between my two daughters for custodianship of this watch.  Both seem clearly agreed that ultimately the watch should fall to one or the other of my very young grandsons.  My older daughter has no plans for children, but she carries the "Foster" name.  The younger one has the two grands.  We talked about how the custodian could, and perhaps should, wear the watch for special occasions in the meantime.  The idea of my son-in-law wearing it came up, because of the fact that it is a gentleman's watch...."