The intro video is the single highest-signal thing on your profile, because it answers the one question a resume cannot: can this person hold a room.
Keep it between two and five minutes. Shoot it in landscape, in a quiet room, with light in front of you rather than behind. A phone is fine. Production quality is not what is being judged.
Cover three things. Who you are and what you teach, in twenty seconds. Then teach one small concept as if the camera were a class, for about two minutes. Then say what you are looking for in your next school.
The most common mistake is reading a script. Principals can hear it immediately and it tells them nothing about how you teach. Speak to the camera as you would to students.
The second most common mistake is skipping it entirely. Verified profiles with a video are shortlisted several times more often than those without.