Dynamic menu highlighting with 3 levels

To have both a top-level page link and its subpage link highlighted dynamically, I’m using the solution described here: https://www.darrenhoyt.com/2008/02/12/creating-two-tiered-conditional-navigation-in-wordpress/

I have a top-level horizontal menu, with subpages in custom sidebars for each top-level page. Some of those subpage menus are nested with two levels.

The highlighting works great, except that when on a child-of-child page I would like for both levels of the subpage menu (ul ul li) to display in the sidebar with the current page highlighted. What I have is just the third level (ul li).

Here’s the code:

<?php if($post->post_parent)
$children = wp_list_pages("title_li=&child_of=".$post->post_parent."&echo=0"); else
$children = wp_list_pages("title_li=&child_of=".$post->ID."&echo=0");  

if ($children && is_page()) { ?>
<ul>
<?php echo $children; ?>
</ul>
<?php } else { ?>
<?php } ?>

Help?