From the French (the OED misses a first, 1917 use by Kipling), gaga suggests the Major in Fawlty Towers, but in the 1920s had this doting sense, which endures in America, where a gaga is the object of devotion, and a drunk; Jonathan Green's book Slang notes that it is both an inexperienced homosexual and deft foreplay.
NO SOONER had Stephen Crook, the Nabokov scholar, escaped Heathrow than his first port of call was the bar-parlour of the Angler's Rest, where he described Ralph Fiennes's visit to the Nabokov exhibition at the New York Public Library. "He'd been flogging his Pushkin movie. I didn't see him but word of his presence spread through the staff grapevine and there was a lot of gaga in the exhibition hall. That's New York insouciance for you."