Boatbums, the conclave for electing a Pope did NOT start in the 13th century...it’s ALWAYS been....sorry you misunderstood.
More accurately, the process has always been electoral.
Over time the rules of electoral eligibility have been refined and the process has been regularized over time as well.
It became a conclave - i.e. a process where the electors are sequestered until they make a decision - in the 1200s.