How do I get tags linking to proper pages (/tag/sample-tag -> pages with that tag)

Found it: The posts I’m working with are instances of custom posts, and the default get_posts() function assumes that posts are just, well, posts. So it wasn’t finding them, and was properly returning “none”.

Solution: I added some code to my theme’s function.php file, like so:

function set_up_theme() {
   ...other stuff
   function mytheme_pre_get_posts ()
      $query->set('post_type', 'my_custom_post_type');
   }
   add_action('pre_get_posts', 'mytheme_pre_get_posts');
}

Better ways or places to set this up are welcome, but it seems to be doing the trick.