My take on it was that Col. Mortimer had the original watch. His sister liked it a lot so he had a duplicate made for a wedding present. It was stolen by Indio on her wedding night and was in his possession for almost all of the movie. TMwNN found Mortimer’s watch snooping through his gear and pocketed it. At the showdown between Mortimer and Indio, TMwNN interrupts Indio’s “when the chimes end” game with Mortimer’s watch. At the conclusion of the game, the Colonel takes his sister’s watch back, and receives his own back from TMwNN, who remarks on the resemblance.
Col. Mortimer’s sister and her husband were murdered by Indio on their wedding night. I’d thought that the watches were a gift from her husband, a matched set for them both. Indio stole hers, but Mortimer got her husband’s, hence it had a picture of her in it.