When are you legally allowed to have 12 players on one team on the field in an NFL game?

According to the NFL rulebook (6-1-1), a team may have 12 players on the field during a kickoff. This can only occur if the ball falls off the tee twice. In that case, the team must bring in a 12th player to hold the ball. However, as soon as the ball is kicked, this 12th player cannot participate in the rest of the play and must immediately leave the field.
https://operations.nfl.com/the-rules/nfl-rulebook/#article-1-free-kick