According to the documentation there's no event attached to that property, but i will give a solution that responds to your use case, add timeout property to your data object as follows :

   data() {

         return {

          snackbar:false,

          timeout:6000,

          ....

         }

    }

add an event handler to your button click :

     <v-btn block

       color="primary" 

       dark

       @click="showSnackbar">

       Show Snackbar

    </v-btn>

in your methods add showSnackbar method

    methods: {

         showSnackbar() {

           this.snackbar=true;

           setTimeout(() => { this.$emit("yourEvent"); },this.timeout);

         }

       }

I simulate a your case in this pen