The Prez/VP run on a ticket. So the Veep is elected. 0 can't run.
If he runs as VP, he’s not getting elected to be the president, so no 22nd Amendment violation. If he later goes on to become president through succession rather than being directly elected to the office, no violation of the 22nd Amendment because, again, he was not elected to that office. He just assumed it after the president stepped down, was removed, or died.
I’m just the messenger folks. It seems clear that the 22nd Amendment was intended to prevent someone who already served two terms from serving again. But this may be a loophole. That’s what loopholes are. They exploit poorly written law in order to go against the law’s original intent.