My read is that impeachment would be the solution. This may be why impeachment can be widely defined.
As to the background check on eligibility, the process is up to the House. Perhaps after this they should pass some rules.
Okay, then we are in agreement, I think, that there is some remedy if a sitting president is found to be ineligible. If the defect is not curable (such as waiting for his next birthday), he would have to be removed from office somehow, even if just declared legally incompetent for office.
You second point is exactly what I’m advocating. This is ridiculous that the country has had these questions swirling — and it will only become more common in the future as people all over the world are more mobile and marry people from different countries and so on. There should be a law defining how to prove a person is fully qualified, a process for evaluating that and certifying it, a procedure for challenging the certification, and a remedy for cases in which the person ultimately is found ineligible.
It is not rocket science. I mean, can you believe in the 21st century the question of whether or not a president-elect is a U.S. citizen essentially is left up to the political parties? You can be damn straight that no one in the House actually asked for any sort of documentary evidence to review themselves.