This clip of Elvis Presley singing 'Trying to Get to You' is from the informal, unscripted segment of his 1968 'comeback' TV special. He was 33 when the performance was taped, at the height of his powers – given the limitations of live TV in the 1950s, this later recording might be the single best way to see what the original fuss had all been about. It's also our first and only chance to see Presley play the electric guitar, which he does well enough here, with considerable feeling. But the Gibson Super 400 that he's playing belongs to the man on his left.

Scotty Moore played guitar in Presley's original and only band, the Blue Moon Boys, and on his early recordings. He started out a country guitarist, a finger-picker in the mode of Chet Atkins. But slathered in echo, that country style translated remarkably well to a rockabilly/rock and roll context, while the context brought something extra – something ecstatic – to the style. Other, extraordinary guitarists were playing rock and roll already: among them Mickey Baker, Lowman Pauling, Johnny Watson and Danny Cedrone, who died just a few weeks before Elvis, Scotty, and Bill Black made their first recordings. Scotty Moore brought something different to the table. Not quite diffidence, but a perfectly worked out sense of proportion. Moore didn't wail, or break from the pack: understated on stage and in person, he played to frame the frontman. (In an interview with Guitar Player magazine, Moore claims never to have broken a string.) All the same, the music's shot through with his playing.

A Gibson Super 400 that Moore had played on early Elvis recordings ended up hanging on a wall at Chips Moman's American Sound Studio in Memphis. Six months after the comeback special, it came down again: Elvis had shown up to record his 15th studio LP. Far and away the best album Presley would make, From Elvis in Memphis owed a lot to the comeback special. The TV producer Steve Binder had managed to cleave Presley away from his parasitic manager, Colonel Parker. ('I'll never sing another song I don't believe in,' Presley said afterwards.) In Memphis, Moman managed to do the same thing and came up with 'Suspicious Minds', 'Long Black Limousine', 'Gentle on My Mind' and other terrific recordings. Like the comeback special, the songs Presley produced then give us our only sense of what he might have accomplished in better circumstances. (In preceding years, Presley had 'backed up so far from the microphone that the engineer would put the mike he was recording on as close to the wall as possible', a backing singer recalled. 'The material was so bad he felt he couldn't sing it.')

As it was, Presley swelled to Brobdingnagian proportions, surrounded himself with sycophants, shook Richard Nixon's hand, and died, in 1977 – the year the Clash released their first album. Chips Moman went on to make other, excellent records – he died a few weeks ago, in his hometown in Troup County, Georgia – and Scotty Moore died this week, in Nashville, taking the mystery of 'Mystery Train' to the grave.

Read more in the London Review of Books

Ian Penman: Elvis looks for Meaning · 25 September 2014

J. Hoberman: Nixon at the Movies · 17 February 2005