His playing career was spent with Atlanta and Rosario Central. As a coach, after winning the championship with Rosario Central in 1973. He had 3 spells and a successful career in the Rosario's club. In the 1980s he soared to the top ranks of Argentine football by guiding Ferro Carril Oeste to two championships, in 1982 and 1984, featuring players such as Adolfino Cañete, Héctor Cúper, Gerónimo Saccardi, Juan Domingo Rocchia, Julio Cesar Jiménez, Oscar Garré and Alberto Márcico.
During his Ferrocarril Oeste days, Griguol would videotape the basketball team, and basketball coach Leon Najnudel would return the favor.
His conservative style made Griguol a non-contender for the job of national coach. He did get a chance to coach River Plate in the mid-1980s, but despite winning the Copa Interamericana in 1987 he was swiftly dismissed when results were not forthcoming and the team's style did not please the fans.
In the 1990s, Griguol took Gimnasia y Esgrima de La Plata under his wing, propelling it to its best harvest ever: two second-place finishes. He would return to Gimnasia twice.
He has also worked in Spain as the manager of Real Betis.
His trademark was a most unusual token of encouragement: he would slap each player in the face before the team entered the pitch. TV cameras caught this ritual more than once.
Timoteo is known mostly by his middle name, or as el viejo ("the old man").