One possible builder is Gerardo di Gerardo. His name appears as a witness to the above legacy of Berta di Bernardo as "Master Gerardo", and as a worker whose name was Gerardo.
A more probable builder is Diotisalvi, because of the construction period and the structure's affinities with other buildings in Pisa, but he usually signed his works, and there is no signature by him in the bell tower.
Giovanni di Simone was heavily involved in the completion of the tower, under the direction of Giovanni Pisano, who at the time was master builder of the Opera di Santa Maria Maggiore. He could be the same Giovanni Pisano who completed the belfry tower.