The year was 1970 and the story has become pop music folklore. Art Garfunkel was jetting around the world to shoot films like Carnal Knowledge and Catch-22 while Paul Simon was moping in New York trying to write songs for the duo's next album. When Art accepted a role in a third film instead of returning to New York as planned, this time to shoot an acid Western somewhere in Central America, Paul flew into a rage. Art tried to explain that it was Joseph Heller's directorial debut, that he would get to play a womanizing caterpillar-wrangler, that principal photography had just begun, and that he'd already learned his line, but Paul would hear none of it.
Art bailed out of Pistol Pocket and booked a flight back to New York to record the album that would become Bridge Over Troubled Water. (The film was never completed for reasons unrelated to Art's departure.)
While Art was en route, Paul felt so bad about denting his buddy's acting career that he almost shredded the bitter songs he'd written in his absence: the one about being the only livin' boy in New York, the one about the long-gone days of harmonizing with "Frank Lloyd Wright." (Art had been an architecture student.)
But when Art walked into the 52nd Street recording studio still wearing the ridiculous mustache [see above] that he'd grown for the Heller flick, Paul, thinking that Art was hedging his bets, was so incensed that he forced him to sing those songs anyway. (Actually, Art simply liked the rugged look he'd suddenly achieved, enjoyed the sense of security it gave him on the subway where he'd previously been taunted by children, and never had a chance to explain to Paul that it was a fake mustache anyway. Somewhere in Central America, a property master was fuming.)
How it ended up on the cover is anybody's guess:
That's funny. In the full image, Garfunkel's got a huge chin, which bears a resemblance to the face of a young John McCain.
I think John McCain was married to Carrie Fisher for a while, so that's another film connection, too.