The Which

[NewHope]

What does "which" refer to in the context below? Does it refer to the fact that "Uncle Raymond and his cronies carried Arkansas for Wallace, our first deviation from the national (Democratic)
ticket"? But it is in different sentence. So I am confused by it.

Context:

On November 6, we learned that Nixon had won and that, as I wrote, “Uncle Raymond and his cronies carried Arkansas for Wallace, our first deviation from the national (Democratic)
ticket since achieving statehood in 1836. . . . I must send my ten dollars to Uncle Raymond, for I bet him last November that Arkansas, the most ‘liberal’ of the Southern states, would
never go for Wallace, which just goes to show how wrong these pseudo-intellectuals can be!” (“Pseudo-intellectual” was a favorite Wallace epithet for anyone with a college degree who
disagreed with him.) I noted that, unlike the South Vietnamese government, I was terribly disappointed that “after all that has occurred, after Humphrey’s remarkable recovery, it has come to the end I sensed last January: Nixon in the White House.”

[Casiopea]

Try looking at it like this, with the relative pronoun weeded out:

that Arkansas would never go for Wallace goes to show how wrong these pseudo-intellectuals can be!

[NewHope]

I understand your explanation as:

that Arkansas would never go for Wallace goes to show how wrong these pseudo-intellectuals can be! = That (that Arkansas would never go for Wallace) goes to show how wrong these pseudo-intellectuals can be!

"That" is the subject here. Am I on the right track?

[Casiopea]

I must send my ten dollars to Uncle Raymon, for I bet him (that) Arkansas would never go for Wallace (but they did go for Wallace), which just goes to show how wrong these pseudo-intellectuals can be.