Cecil traces the use of “bananas” to mean crazy to 1968, but ignores the 45 rpm release of the novelty song “Loving You Has Made Me Bananas” by Guy Marks, which failed to crack the Top 40 but did receive some AM radio airplay. I certainly remember hearing it.
According to 45cat.com (http://www.45cat.com/record/4511055), this single was released in March of 1968, which means it would have been recorded at least a month or two earlier. So it seems likely this would predate the University of South Dakota publication Cecil references as a first citation.
Just to add a twist: I still see “fruit” and “fruity” used in the sense of “weird” or “bogus”, e.g., “The claim that the Mafia murdered JFK seems fruity to me.”
I find myself cringing because of the obsolete, or at least obsolescent, use of the term as a homophobic slur. I can’t develop a consistent “ethos” for this phenomenon: I still find “fruity” repugnant enough to wish users would find a different term. OTOH, I’ll keep using “tar baby” until I find an acceptable idiomatic substitute.
I found a couple more early examples of “going bananas”:
From “Woman is Held in Drugs Counts” (page 14 of the October 30, 1954 Providence Journal): “Mrs. Poitras testified that when she introduced [Mr. Arsene] Dextraze to Mrs. Fitzgerald, the musician described his supposed need for narcotics by saying he was ‘going bananas’ and that ‘the walls are closing in on me’.”
From a column by Art Grace, “Mounts Scarce, But Barry Hasn’t Lost Confidence” (page 15A of the December 7, 1965 Miami News), horse jockey Barry Pearl was quoted that he also participated in drag racing, because “You do the same thing every day and you start going bananas.”
Yes, that usage requires it to be significantly older, though fifty years later I cannot suss the meaning of, “Father has the ship-fitter blues,” without wondering how it got airplay. Unless the same program managers who let, “Good golly, Miss Molly, you know you sure like to ball,” on the air were still as stupid/assuming listening parents were stupid as to not complain. Yeah, FTR some did, but still.
The cover for allowing that was that “ball” also had the sense of “to dance” (cf. “Ballin’ the Jack”). And the context of the surrounding lyrics in “Good Golly Miss Molly” reinforced this (“From the early, early morning to the early, early early night, when you see Miss Molly rockin’ at the House of Blue Lights”).
That’s not to say the naughtier meaning wasn’t also implied, but double-entendres had by then had a well-established legacy in blues and R&B for many decades.