The thing is, if Obama is not eligible, then he is not President, and thus cannot be "removed" by the usual House Impeachement/Senate trial process Therefore if he were declared to be ineligible, the process laid out by the 12th and 20th amendments would have to be followed.The 20th amendment clearly says that if a President shall not have qaulified, the VP shall ACT as President, until a President shall have qualified. The 12th amendment gives the process for that.
The idea that the first runner-up in a presidential election could become president if the office became vacant, was scrapped pretty early in our history.
What was discarded early on, by the 12th amendment in fact, was that the runner up would become VP. Biden was elected VP, not President. The VP becomes President if the President dies or is impeached and removed. That would not be the case for an ineligible usurper.
You are putting the cart before the horse. Congress is the only body that has the Constitutional authority to indict (impeach), investigate, and bring the president to trial once he has been elected and sworn in. Until the president resigns or in found guilty in the Senate, he IS the president. Again, see de facto officer doctrine.
Biden was elected VP, not President. The VP becomes President if the President dies or is impeached and removed. That would not be the case for an ineligible usurper.
Either you can back that up with more than just your intuition, or you're making it up.