My question is specifically asking for the Hadith of the blessed praised Prophet (Sallallahu Alaihi wa Sallam) of Allah on this matter. If I recall correctly it states something in the effect that this assembly of influential council composed of the Muslim distinguished scholars, and notables who will be able to attend a general meeting to be held for this purpose are suppose to gather within 3 days after the death of any one of the Khulafa' and to hold an election for the Khalifa.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

We have not come across any Hadith ordering or urging Muslims to get together in a given place for three days and not to leave that place for any purpose whatsoever before choosing their Caliph (leader).
In fact, Muslims are asked to choose their Caliph (leader) as soon as possible, i.e. before any conflicts emerge between them.
Allah knows best.