"No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States."
The Constitution clearly states that a person needs to be 35 years old to be eligible for the office.
A mentally ill person may have under-developed brain. In particular, a 70 year old person may have brain of a teenager. The spirit of Constitution is to deny the Office of the President to this person.
The federal government needs to implement policy to perform the corresponding medical checks on the President Elect.