Without Google Tag Manager

To start tracking the use of the webchat you have to listen the events sends from the bot.

window.clustaarSettings = {
            bot_id: YOUR_BOT_ID,
            bot_token: YOUR_BOT_TOKEN,
            eventListener: clustaarEventsListener
};

Then you can add your tracking for each events. See the list of events sends from the bot here

function clustaarEventsListener(eventName, payload) {
  switch(eventName) {
    case "CLSTR_USER_INTERACTED": {
      analytics.track('User interacted with the webchat');
      break;
    }
    case "CLSTR_USER_LINK_CLICKED": {
      analytics.track('User click on a link', {'label': payload.label, 'url': payload.url})
      break;
    }
  }
}