[El Gato]

They swear an oath to defend the Constitution, not the president.

If he's ineligible, he's not the President. However I'm sure they'd have to see proof. Maybe they should be looking for it? Maybe they are?

[Star Traveler]

You said — If he’s ineligible, he’s not the President.

—

But, until “he’s not the President” — “he is the President”... :-)