Sorry but the Constitution DOES cover this exact situation. Granted, it took a couple of Amendments, but it's pretty cut & dried.
The 12th Amendment reads in part:
But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.
And the 22nd Amendment clarifies the eligibility issue:
No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once.

OCU