How to Properly Use Vue Router beforeRouteEnter or Watch to trigger method in Single File Component?

I'm working on an app in Vue.js using Single File Components and Vue Router. I have a Search component where I need to execute a method to re-populate search results each time a user visits the route. The method executes correctly the first time the route is visited because of the "create" hook:

created: function() {
    this.initializeSearch();
  },

However, when the user leaves the route (to register or log into the app for instance), and returns to the Search page, I can't seem to find a way to automatically trigger this.initializeSearch() on subsequent visits.

Routes are set up in index.js like so:

import Search from './components/Search.vue';
import Login from './components/Login.vue';
import Register from './components/Register.vue';

// Vue Router Setup
Vue.use(VueRouter)

const routes = [
  { path: '/', component: Search },
  { path: '/register', component: Register },
  { path: '/login', component: Login },
  { path: '*', redirect: '/' }
]

export const router = new VueRouter({
  routes
})

I gather that I should be using "watch" or "beforeRouteEnter" but I can't seem to get either to work.

I tried using "watch" like so within my Search component:

watch: {
    // Call the method again if the route changes
    '$route': 'initializeSearch'
  }

And I can't seem to find any documentation explaining how to properly use the beforeRouteEnter callback with a single file component (the vue-router documentation isn't very clear).

Any help on this would be much appreciated.