An email from veteran "oddball" collector Larry Serota (the stuff he collects is "oddball," not Larry) tipped me to an uncataloged premium picture being offered on eBay.
The item was a black-and-white, blank-backed 8" x 10" picture of L.A. Dodgers outfielder Carl Furillo. The sponsor is TV Treat ice cream. A couple of the company's packages are featured in a baseball design at top-right.
The endorsement bearing Furillo's facsimile signature reads: "TV Treat / a hit everytime". In beat-up condition, the photo sold for $55.
In researching the premium, I found on a website called Sandy Koufax Time Capsule (www.sandykoufax32.com) a similar picture of Koufax scooping out a spoonful of ice cream and including the same endorsement.
That picture is attributed to 1959, so the issue could actually be from either year. It probably can't be pinpointed unless or until other player premiums are found.