Google Adsense internal search code does not work with Drupal sites normally. The reason is $_GET[q] conflict between both services. $_GET[q] means "current page" for Drupal and "search query" for Google. We can fix it with two easy steps.
Create a custom page like "websearch" etc under Drupal and add Adsense Code for results page.
Add this code at the top of your Drupal's index.php:
// Fix Drupal-Adsense conflict
$_GET[q] = ($_GET['cx']) ? "websearch" : $_GET[q] ;
Thanks, it worked! That was a quick fix compared to all of the longer methods I have seen previously.
All ingenious is simple.
You can try to use
var googleSearchQueryString = "z";
parameter for search results. And don't forget to change this input name in search form, ofcourse.