[Vuejs]-How to fire an event on Vue switch change

I would recommend using a 2-way computed property for your model (Vue 2).
Attempted to update code here, but obvs not tested without your Vuex setup.
For reference, please see Two-Way Computed Property

data: function(){
  return {
    noAvailableMonitoring: false
  }
},
computed: {
  report() { return this.$store.getters.currentReport },
  isBeingMonitored() { return this.$store.getters.isBeingMonitored },
  availableMonitoring() { return this.$store.getters.checkAvailableMonitoring },
  toggle: {
    get() {
      return this.$store.getters.getToggle;
    },
    set() {
      if(this.availableMonitoring) {
        let dto = {
          reportToken: this.report.reportToken,
          version: this.report.version
        }
        this.$store.dispatch('TOGGLE_MONITORING', dto).then(response => {
        }, error => {
          console.log("Failed.")
        });
      } else {
        this.$store.commit('setToggle', false);
        this.noAvailableMonitoring = true;
      }
    }
  }
}