Search box in custom (404) page

Is there any simple way to put search text field to some other page than full page search? Thanks in advance.

[update]Simplest way I’ve found is to use {{search-text-field}} component in custom handlebars template and then define search action on controller:

import DiscourseURL from 'discourse/lib/url';

export default Ember.Controller.extend({
  
  actions: {
    search() {
      let searchTerm = this.get('searchTerm');
      DiscourseURL.routeTo('/search?q=' + searchTerm); 
    }
  }
});

Is there any way to modify default text (search topics, posts, users or categories):