Under what condition will the head coach be ejected for a repeat violation?

The correct choice is based on the understanding of how repeated violations of specific rules can escalate in severity, particularly concerning equipment violations like using an illegal bat. If a team uses an illegal bat, it constitutes a serious violation of baseball rules because it can impact the fairness and integrity of the game.

When an illegal bat is discovered, it not only penalizes the player but also reflects on the team's adherence to regulations, which implicates the responsibility of the head coach. If this violation occurs again, it shows a pattern of disregard for the rules, leading to the potential ejection of the head coach. This policy exists to ensure coaches maintain a standard of compliance concerning player conduct and equipment.

In contrast, while other actions such as disputing an umpire's call, arguing with another coach, or a player stepping out of the batter's box can also lead to consequences, they typically do not carry the same weight or severity in terms of a direct threat to the game’s integrity as the use of illegal equipment does. Hence, the repeat violation of an illegal bat is the condition that would lead to the coach's ejection.