Jitsi for Empathy Talks -- use case for covid19 isolated people

I’m thinking of another use case. This case is bringing an empathy walk to jitsi.

The basic use case is that two people (just two, and only two) meet.
The meeting lasts an hour and the first 20 minutes is for the first person and the next 20 minutes is for the second one. The last 20 minutes is for reflections.

How can I invite just two people to a jitsi meeting and create a workflow like this? I mean having a timer or clock that tick mute and unmute with popup messages?
I was thinking to put the meet embedded in a page and have then all the empathy talk coordinated from the outside, but can it be done inside?

thanks

Starting from a code like this:

<html itemscope itemtype="http://schema.org/Product" prefix="og: http://ogp.me/ns#" xmlns="http://www.w3.org/1999/html">
    <head>
        <meta charset="utf-8">
        <meta http-equiv="content-type" content="text/html;charset=utf-8">
    </head>
    <body>
        <script src="https://meet.jit.si/external_api.js"></script>
        <script>
            var domain = "meet.jit.si";
            var options = {
                roomName: "JitsiMeetAPIExample",
                width: 700,
                height: 180,
                parentNode: undefined,
                configOverwrite: {},
                interfaceConfigOverwrite: {
                    filmStripOnly: true
                }
            }
            var api = new JitsiMeetExternalAPI(domain, options);
        </script>
    </body>
</html>