Why the room should see the clock
A timer only the chair can see turns them into the clock police. Someone has to interrupt, and nobody enjoys being the one who does. Put the same timer on the shared screen and the time becomes a fact the whole room is looking at. People wrap up on their own.
Give each topic its time before it starts. Ten minutes for a decision, five for a demo, whatever the agenda allows. Then start the clock when the topic starts, not when someone remembers.
Zero is a moment to decide, out loud and in one sentence. Either you finish now, or you agree to take five more minutes from something specific. The trouble starts when a meeting drifts past zero without saying so. That time comes from the last item on the agenda, which is usually next steps. This timer keeps counting into overtime for that reason: the overrun stays on screen instead of vanishing at 00:00.
