Elvis wore the watch during live performances at the Louisiana Hayride and TV performances on the Dorsey Brothers and Milton Berle Shows and can been seen in the Jailhouse Rock promotional shots.
The story of the watch.
On April 25, 1956, Elvis Presley, Bill Black, Scotty Moore, And D.J. Fontana were sitting near the pool at the New Frontier Hotel in Las Vegas when a Jeweler approached Elvis with a jeweled watch as a gift for him. Elvis took off the watch he was wearing, saw that Scotty was not wearing a watch (he had broken the band on his) and gave his old watch to Scotty.
Scotty kept the watch in his possession from then to the mid-90's at which time He had the watch cleaned and repaired and gave it as a Christmas gift to Ronnie McDowell. This is the actual watch worn by Elvis and given to Scotty Moore on that date
(Source: eBay / HA Auctions / FECC)