The BBC1 television recording below from January 16, 1985 shows the moment during a rerun of Star Trek that the film breaks. (The episode is The Return of The Archons.) It's the perfect storm of incongruity and dissonance: Sulu's monologue, the glitch of the torn film, the unplanned announcement, the words "Temporary fault" across the still frame of Kirk and Spock, and the groovy library music.
At r/ObscureMedia, TheUpperHand identifies the song as "Westcoast Trip" by Parry Music.
As Sulu said, "It's paradise, my friend."
Previously:
• The man who saved Star Trek has died
• This 24-hour recording of idling engine noise from a Star Trek ship in Star Trek will put you to sleep