The Twelfth Amendment specifies:
The person having the greatest number of votes as Vice-President, shall be the Vice-President, if such number be a majority of the whole number of Electors appointed, and if no person have a majority, then from the two highest numbers on the list, the Senate shall choose the Vice-President; a quorum for the purpose shall consist of two-thirds of the whole number of Senators, and a majority of the whole number shall be necessary to a choice.
This choice is made by the incoming Senate, but before the outgoing Vice President has left office. Presuming that A) The election is inconclusive and gets sent to Congress to resolve, and B) the incoming Senate is split 50-50 between parties (or at least votes that way), does the outgoing VP get to break the tie?