Closed Session During a Webinar

I need to be able to temporarily pause a webinar during a meeting for a closed session. I need to make sure no panelists or attendees can see or hear anything during the closed session (there will be in-person attendees who will be participating in the closed session). I tried it last month and it did not work. I paused the recording and muted the laptop but remote participants reported they could still hear the closed session conversation. I unpaused the recording after the closed session and I ended up with two separate videos instead one one with a pause in the middle.