Vance will probably publicly kneel and pray to Trump's AI powered robot-doll in order to gain legitimacy with the MAGA faithful and, I'm sad to say, but this will likely work. He will then declare a years long national period of mourning while implementing Peter Thiel's plan for global destruction.
I think a post-Trump Vance presidency looks like Vance wrapping himself in Trump flags and flanking himself with Trump posters and maybe even wearing Trump merch. He'll definitely be seen in red MAGA hats or even red MAGA onesies, anything to distract from the fact that he's a known couch fucker.