Add Login and logout buttons to top menu bar

“PRIMARY” and “secondary” menu bar really don’t mean anything when used out of context and without explanation. However, (guessing a lot) if your menus are constructed consistently you should be able to find the ‘name’ of the second menu and add a condition like (overly formatted for readability):

if (
  is_user_logged_in() 
  && (
    $args->theme_location == 'menu_top' 
    || $args->theme_location == 'other_menu_name'
  )
) { 
    $items .= '<li><a href="'. wp_logout_url() .'">Log Out</a></li>';

Same with the elseif.

Look for a call to wp_nav_menu in your theme files to find the ‘name’ of the second menu.