[GregNH]

It appears that most historians, constitutional scholars and political scientists interpret “qualifying” or “failing to qualify” as being related to acquiring a majority of the electoral votes.

Can you point to one historian, constitutional scholar, or political scientist that has said this?

[Nero Germanicus]

See the link in post 103 above and here’s another to the Heritage Foundation’s Guide to the Constitution, 20th Amendment.
http://www.heritage.org/constitution/#!/amendments/20/essays/182/presidential-terms
The Heritage Article quotes Professor Akhil Reed Amar of Yale Law School and the excerpt from the book is authored by Alexander S. Belensky, Visiting Professor at M.I.T.

There is also the Congressional Research Service Report: “Presidential and Vice Presidential Succession: Overview and Current Legislation”
https://www.fas.org/sgp/crs/misc/RL31761.pdf