I don't think he would go up against Pence. But then, I would think Pence would almost automatically pick him as VP.
Well, in looking at the two personalities, I'd say Pence would easily be run over like a freight train from the left and I see Cruz displaying some back bone. If indeed he is running in 2024 I think he would challenge Pence if Pence ran, and based on the ground game that he had when he ran for the Senate and in '16, I'd say he's already made plans and knows what he needs to do to stomp on the left. If he doesn't see a clear path to victory, I don't see him running because he doesn't want to deal with all the mud slinging and the leftists obstruction. I've even thought, if Trump isn't re-elected, he may drop out of politics altogether. Just my opinion.
It's not going to happen, but I would love to see Trump select Cruz over Pence as his new VP. (I know, in my dreams).