I haven’t found anything earlier that brings up this question, but although the resolution was clever, it didn’t satisfy me, and (though I could be wrong) I think Brown misses the fact that at one point there should be two copies of the object in existence at the same time. In any case, this was the first part of a pair of short-short stories in the Feb ’54 Galaxy, which together were called Two-Timer (the second of which had no time travel).
The story was reprinted in the 1958 collection, Honeymoon in Hell, which features a cover by Hieronymus Bosch (indexer Grzegorz’s favorite painter) with an owl in the background (Grzegorz’s favorite bird)!
When the story was reprinted in Nightmares and Geezenstacks it was presented as three separate vignettes (“The Short Happy Lives of Eustace Weaver,” Parts I to III), but the original EQMM publication had just one entry (Of Time and Eustace Weaver) in its table of contents.