This extraordinary indication is how Beethoven describes the third movement of the "Moonlight" Sonata. It is how Brahms designates the last movement of his Op. 108 Sonata in D minor for Piano and Violin.
Reading it in the light of having thoroughly worked out a definition of what makes the music truly agitated, as opposed to frantically fast and never fast enough, the Brahms movement becomes elegant, playful, inviting, rich in contrasts that recall those in the Beethoven movement.
May I remind you of the not-quite-definition of agitato in Koch's Musiklexicon (1802) which states that, there being plenty of words to designate fast, agitato must mean something else. I take it to indicate beats against beats, usually three's where least expected.
So, too, presto means more than fast: It means that the smallest note value in the piece is the beat. Thus, here, in 6/8, instead of two relentless-never-fast-enough beats in the bar, there are 6, a number far more conducive to internal turbulence. Try it.
