Managing breakout sessions

I am a Zen meditation teacher who uses Zoom to reach my group. On Sundays during services, we do meditation for two 30-minute periods. It is during that time that traditionally, the teacher meets with students for one-on-one interviews in private. Breakout sessions seem like a good way to do this, but as I understand it, even if you have a session with only one person, it needs to be set up in advance. It would mean having all students at least assigned to breakouts, one-on-one with me. But, I don't understand how to 1) start as session during the silent meditation period without disturbing attendees, 2) signal to the next student that it is his or her turn to join me in the breakout session, and finally 3) given that my teacher may want to also occasionally offer such meetings, how to set him up as the host of those sessions that he would take part in, one-on-one.