List children of second level sub page

Top Level Page

- Second Level Page

--- Child Page

--- Child Page

--- Child Page

The goal here is to list all children of second level, I have that done from the codex. However, when I click on a Child, the children should still display because we're technically still inside of the Second Level.

<?php
// Globalize the $post variable;
// probably already available in this context, but just in case...
global $post;
    wp_list_pages( array(
        // Only pages that are children of the current page
        'child_of' => $post->ID,
        // Only show one level of hierarchy
        'depth' => 1
    ) );
?>