New Twiddle

components.my-component.js

import Ember from 'ember';

export default Ember.Component.extend({
  tagName: ''
});

components.my-component.my-component-impl.js

import Ember from 'ember';

export default Ember.Component.extend({
  count: 0,
  
  click() {
    const count = this.get('count') + 1;
    this.set('count', count);
    this.$('p').text(`You've clicked me ${count} times`);
  }
});

controllers.application.js

import Ember from 'ember';

export default Ember.Controller.extend({});

templates.application.hbs

<button {{action (mut shouldRender) (if shouldRender false true)}}>
  Toggle
</button>

{{my-component shouldRender=shouldRender}}

templates.components.my-component.hbs

{{#if shouldRender}}
	{{my-component/my-component-impl}}
{{/if}}

templates.components.my-component.my-component-impl.hbs

<p>Click me</p>

twiddle.json

{
  "version": "0.12.1",
  "EmberENV": {
    "FEATURES": {}
  },
  "options": {
    "use_pods": false,
    "enable-testing": false
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "2.12.0",
    "ember-template-compiler": "2.12.0",
    "ember-testing": "2.12.0"
  },
  "addons": {
    "ember-data": "2.12.1"
  }
}