Earlier, I mentioned a 1989 interview in which Zappa described a performance by John Cage:
A short time after that, John Cage came to Claremont College and he was giving one of his … he does these performances with a throat microphone. He’d put this thing on his throat and drink a quart of carrot juice, or read something to you while he was drinking the carrot juice. 
I suggested that Zappa was referring to a concert he attended at Bridges Hall at Pomona College (in Claremont, CA) on March 7, 1962 in which Cage and David Tudor performed Where Are We Going? And What Are We Doing? and Variations II. Neither of these pieces fits the carrot-juice description, so I thought I’d look into it a little more.