Presidential Elector Math

Here's a question that I've been pondering. Suppose that two presidential electors turn out to be ineligible under the rules of Article II but this fact is unknown until after they vote. Would the winner then require only 269 votes or 270? In other words, do you calculate the majority based on the total number of electors or the total number of eligible electors? There is no relevant precedent, though the issue almost came up in 1876.

The text of the Twelfth Amendment says that the winner is the person who receives "a majority of the whole number of Electors appointed." That probably means that it doesn't matter if the people appointed are eligible to be appointed. But you could say that the appointment of an ineligible person is void if the person is not replaced prior to voting. (If an elector died right before the electors vote, an alternate presumably must be picked for a state to receive its full share of votes.)