Custom Theme Template Wont Show After Adding Endpoint To Author Page

I am trying to get my custom gallery.php used when someone navigates to example.com/author/authorname/gallery.

Through a previous thread I was able to use the following code to rewrite the endpoint:

add_action('init', function() {
	global $wp_rewrite;
	add_rewrite_rule(
		$wp_rewrite->author_base . '/([^/]+)/gallery/?$',
		'index.php?author_name=$matches[1]&_auth_gal=1',
		'top'
	);
});

add_filter('query_vars', function($vars) {
	$vars[] = "_auth_gal";
	return $vars;
});

/**
  * tells whether we are in the author/^/gallery/ screen
  * use get_the_author_meta( 'ID' ) to get the author ID
  *
  * @return bool true|false
  */

function se_is_author_gallery() { return "1" == get_query_var('_auth_gal'); }

After ensuring I flushed the rewrite rules, and adding this code to the template theme file, I am still not able to get example.com/author/user/gallery to show up with the gallery.php template. Instead, it simply loads the same template as example.com/author/user/.

If you have any suggestions, advice, or feedback it would be greatly appreciated. Thank you so much.