Jesus didn't *elect* anyone. He spent the night in prayer before selecting them.
Would that be sufficient scriptural evidence?
Mention of it by Jesus or Peter about the specific office and/or specific instructions on how to fill that office upon Peter's demise.
IN the seven letters to the churches in Revelation, there's certainly no mention of a central authority to which they all answered.
Jesus addressed the local congregations individually.
“Mention of it by Jesus or Peter about the specific office and/or specific instructions on how to fill that office upon Peter’s demise.”
Mention of the office, that’s back in Matthew 18. “I give you the keys to the kingdom of heaven.”
Specific instructions, did you read Isaiah 22:10? It explains that when Christ gave Peter the Keys to the Kingdom of Heaven, that the office was to be passed down to his successors.
How it gets passed down: Acts 1.
Seems to me multiple issues here, the first being the office of the pope. That needs to get settled first.