That raises an interesting question.
Let's say that the Hamilton electors vote for someone other than Trump for President, but Pence for VP. Trump gets under 270 votes, but Pence gets 270+.
So, the election of the President goes to the house, but Pence has, at this point, officially been elected Vice-President.
If the House then appoints Pence as president, what happens to the Vice Presidency?
Edit to add: Never mind, can't happen, unless the Electoral College's protest votes go to Pence.
In this event, the House of Representatives is limited to choosing from among the three candidates who received the most electoral votes for president. Each state delegation votes en bloc – each delegation having a single vote; the District of Columbia does not receive a vote. A candidate must receive an absolute majority of state delegation votes (i.e., at present, a minimum of 26 votes) in order for that candidate to become the President-elect. Additionally, delegations from at least two-thirds of all the states must be present for voting to take place. The House continues balloting until it elects a president.