Interesting responses so far. We're missing the most obvious one, an apolitical person with the last name Wallace who just wanted to share last names with the president
A more serious scenario is a working-class white person who got into socialism at a young age, perhaps during the depression, and saw Wallace as a "step in the right direction". During the 1950s red scare they lost their left wing touch but still remained economically populist/anti-big business. During the Civil Rights movement, race resentment politics had an effect on them. They didn't like Humphrey's/LBJ's focus on civil rights, and didn't trust Nixon who they saw as too business-friendly, but Wallace's mix of economic populism and racism appealed to their sensibilities.
Essentially, this would be the Greatest Generation version of a WWC Sanders-Trump voter.