Would and/or Should Hillary choose Bill as VP

[The Other Castro]

Ineligible to be both. I then briefly considered him serving in her cabinet, making him part of the presidential line of succession. However, he still couldn't become president that way, just like someone under 35 or not a naturally born US citizen couldn't, even if they were in the cabinet, like former Labor Secretary Elaine Chao.

As Morden said, this discussion has been had on the Consitution and Law page showing that he is in fact eligible to serve. He is not eligible to be elected, which is a huge difference. Eligible to serve is being 35+, natural born citizen, resident for 14+ years. Eligible for election is not having been elected twice already (or once and more than half of another term through succession). He could be elected VP as he only needs to meet the eligibility requirements to serve, not to be elected.

[The Other Castro]

22nd Amendment -- no person shall serve as President who has served two terms as President. No person shall be Vice-President who is ineligible to be President.

Incorrect, the 22nd Amendment says "No person shall be elected to the office of the President more than twice."

12th Amendment: "No person constitutionally ineligible to the office of President shall be eligible to that of Vice President of the United States."

The 12th Amendment notes ineligibility to the office, but not to election to the office. The only eligibility requirements for serving in said office are found in Article II, Clause 5 of the Consitution, which are listed as being a natural born citizen, 35 or older, and 14 years a resident.