in your first sidebar is code that checks to see if the page is the home page and assigns a variable.
<div id="sidebar">
<?php if (is_home()) { $check_home = '1'; } else { $check_home = '0'; } ?>
in the second sidebar, and i'm assuming this is the one missing, it checks the variable.
if you want the second bar to appear on all pages you need to take out the if statement
<div class="sidebar_right">
<?php if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar(2) ) : ?>
<?php include (TEMPLATEPATH . '/searchform.php'); ?>
<?php /* If this is the frontpage */ if ($check_home == '1') { ?>
<?php get_links_list(); ?>