Considering his ego, the only time he likely would have accepted being the running mate would've been in 1964 with Goldwater, but I can't imagine Goldwater ever offering him the slot. For any even semiplausible scenario in which Wallace becomes VP, you'd need either him to not decide after losing his first gubernatorial race that he'd never again be outnig
gered yet still eventually become governor, have a different head of the Presidential ticket than real life, or both. A less racist Wallace might have been paired with with HHH or RFK in 1968 on the Democratic ticket.