The prototype fretless guitar, made in the 1960s, appeared in Sunday's show.
Its current owner recorded sessions for a film company co-founded by Harrison, who asked him to play the guitar.
"I played a few notes and he said: 'Yeah, you're definitely getting more out of it than I am. It's doing better for you, why don't you have it'."
Bartell's of California made the instrument, which the owner, Ray, described as "a strange old thing to play".
A photograph in the episode shows the guitar among Harrison's collection.