Pence does not have any power to choose electors and does not have any type of tiebreaker capability. The narrative that Pence will save the day is hopium mixed with ignorance.
http://electoralcollegehistory.com/electoral/crsmemo.asp
He presides over the process but does not have a vote. A dispute is raised by a Senator and a Representative. The two chambers then have two hours to sort it out. If the chambers still have a dispute then the electors selected by the respective governor are used.
The naming convention is amusing me. Waiting for the counterclockwise rimjob and clockwise rimjob