I don’t have to find an “if he is found to be ineligible” clause. Just look at the Constitution. It has clear instructions on how a bill must be passed into law as well as who is eligible to be president. Only a duly sworn, eligible president can sign a bill into law. Not a usurper. Besides, if it is found that the zero is ineligible and for some reason the courts and Congress refuse to remove him from office, there WILL be a rebellion.
That's just the point. He'll never be "found" to be ineligible. A "finding" comes from a court proceeding. No court will ever hear this case.
"Only a duly sworn, eligible president can sign a bill into law. "
Again, this language is no where in the USC. What's described in the Constitution is the "President". Obama is clearly the President. He met every check that the Constitution enumerates. He was elected by the Electors that are certified by the state they represent. There isn't any proscribed procedure in the USC to mount this kind of challenge. Because of this, again no court will ever hear any challenge to a law or order based on Barry's qualifications, or lack thereof. Any speculation otherwise is pure folly.
The USC points out very clearly what the minimal qualifications are for POTUS. Unfortunately, beyond certification of the Elector (as briefly mentioned in USC as "which they shall sign and certify"), there really isn't any procedure outlined in the USC about examining those qualifications much less any indication whose responsibility it would be.
The USC is not perfect. Perhaps an Amendment is in order here to give some clarification and specificity to this issue.