How can I enable or disable the secondary links menu programmatically?

Borrowing from snippets I've found in contributed themes, it seems that one way would be a bit of conditional php. If your theme is already printing the $secondary_links variable in page.tpl.php you can try the below.

<?php
   global $user;

  if (!$user->uid) {
     /* IF USER NOT LOGGED IN DO "THIS" ie: not print $secondary_links */
  }
  else {
   /* IF USER LOGGED IN DO "THIS" ie: print $secondary_links */
  }
?>

note the orange text and insert what you need.