Jesus didn’t have to scour the Scripture because He is the Word of God.
First of all, the Old Testament is written history. Then it is prophetic.Those prophecies were given to certain Jews and are precise. The Word is always precise.
Jesus spent His life , from the moment of conception, taking deliberate steps to fulfill prophecy.For Him, He knew what to do, when to do it, what to say, after all, He was there before the foundation of earth.Between free will (think Peter with the sword trying to stop His arrest by the Romans) and Satan doing whatever he could to have Jesus NOT die on that cross(think the reluctance of Pilot to crucify Jesus) (and there are other incidences in the NT), Jesus had to deliberately make sure He fulfilled everything exactly.
And the OT speaks twice as much to the Second Coming as to the First, so it will be extremely exciting to see this too fulfilled precisely as Written.