Not the very guitar owned and played by Elmo'...it's the model that he played. There's one available on eBay now and the photos are fairly good. The price is reasonable today (Friday, April 12 at 10:24 p.m.) but may get above what a refin with replaced tuners could possibly be worth... Info from silvertoneworld.com:
"The 1361 and 1363 were a couple of odd birds that Sears offered for only one catalog, Spring/Summer 1954. Danelectro soon provided their first electrics in Fall/Winter '54, and Sears was happy to offer up the Silvertone 1375 & 1377.
The 1361 and 1363 guitars are a bit of a mystery. The catalog illustration looks like a Harmony H44. The actual guitar examples that I've seen, however, look very much like a Kay-made guitar, something like a K-141/142. Mystery aside, they were some of the very first true solidbody guitars offered by anyone, anywhere.
These were some of the first attempts at production solidbody guitars, and show an amazing degree of sophistication, both in the very Les Paul™like body shape, and the single piece neck and body, with the sides added on much like Les' original 'Log' prototype electric guitar. Needless to say, these are exceedingly rare, especially the 2-pickup 1363."
Caution: this one on eBay has been refinished and has replacement tuners: