My Headmaster was a JP and was often absent. On such occasions, it was not uncommon for people to have to wait an hour or more, or even be sent away and told to come back at a later time. Alternatively, one of the two senior Masters authorised to use the cane, might be summoned to deal with those waiting. But again, during this period there was no certainty that punishment was due, so I would exclude this time.
Once in the office, there was a brief inquisition, if guilt was admitted / established, a succinct explanation of why the behaviour was not acceptable was delivered and punishment followed straight away and concluded with a phrase such as “I don’t want to see you in here again Weston”.