When I go to advanced search and choose a manufacturer without putting in a search query (because I just want to search the store for the manufacturers products) I get a results page with products_search.php. This is correct.
 
However when I click on "Next" for page 2 and on it uses products.php with url query strings attached. It does continue to filter by manufacturer but I get the layout settings for products.php (regular products pages).
 
This happens for any search filter (like categories) if there is not a search string (search_string= in url)