That would not be directing him to vacate the office, but yes he could probably do that. But he wouldn't elect Musk, he could nominate Musk. He'd still need Congress (beholden to Musk for their future seats if GOP) to confirm him. But you also have to be qualified to be President to be Vice President, so Musk would be disqualified anyways.
Who is going to disqualify him? Republicans would just invent some doublethink for why it is okay for this particular African to have that role. The extremely partisan SCOTUS will allow it, and that will be that.
If SCOTUS says it's ok, then the US Constitution is completely tossed out and SCOTUS has no authority to say anything. That's not to say they wouldn't make a decision like that, but to disregard the literal text of the Constitution would make both Congress and SCOTUS unnecessary, they can be scrapped in seconds with an EO after a decision like that.
They'd pull the same stunt that they did for Trump. If Trump had been convicted for the Jan 6th riot, that would've disqualified him from becoming president. So SCOTUS dragged out the appeal that reached them. Then their decision made it ridiculously burdensome to continue. If Musk were nominated as vice president and somebody sued, SCOTUS could drag out that case past the end of the term. Then they'd drop it as moot.
We've already had that decision, last year. Trump v. Anderson. Per the Supreme Court, if Congress doesn't explicitly call something out down to the last detail and already have anyone potentially impacted on double-secret probation, then oops, too bad, nothing anyone else can do to enforce the Constitution.
The Vice-President and President need to meet the standards in the Constitution? Did Congress pass a law establishing how those standards are to be judged and enforced? No? Guess they don't matter then. If Congress wanted, it could pass a law and Trump could sign it. Unless that happens, the Constitution is just unenforceable. ¯\_(ツ)_/¯
In Russia they say, "we have lots of laws, just no one pays any attention to them". Russia is a law-less State. Concur with how things are progressing now in USA. Congress and Senate both subverted by too many voters being deceived by D. Elections not well-informed, so not actually functional.
Sure, and I'd default to assuming the % in the military is always higher because they're trained to follow orders.
But if anything makes some among them say "to allow this would be to violate my oath to support and defend the Constitution of the United States against all enemies, foreign and domestic", then disregarding the constitution would be it.
I'm not saying the administration wouldn't try it. I am suggesting that it may lead to a demonstration of how NIJ RF3 doesn't stop 120×570mm NATO.