When VPs become relevant?

Hi, first post in this community. I was reading the other day than Vicepresidents were traditionally isolated from the decision-making of various administrations (with the symbol of LBJ). When, would you say, this change? I remember with Biden as VP they said that he was always, in the big moments, the last person in the room with the President, would you say this change with him, Cheney or before?