API Google: Custom Search desde otro buscador

pag1.php:
<form action="buscador.php">
     <input type="text" name="qBuscar">
     <input type="submit" >
 </form>

buscador.php:
<script src="https://www.google.com/jsapi" type="text/javascript"></script>

<main>
<section class="wrapper">
<h1><span>SEARCH</span></h1>
  <div id="contain">
<script>
  (function() {
var cx = 'XXXXX64100774925828:bdugbl_aie4';
var gcse = document.createElement('script');
gcse.type = 'text/javascript';
gcse.async = true;
gcse.src = 'https://cse.google.com/cse.js?cx=' + cx;
var s = document.getElementsByTagName('script')[0];
s.parentNode.insertBefore(gcse, s);
  })();
</script>
<gcse:search></gcse:search>
  </div>
</section>
</main>

<script>
setTimeout(function(){
  $('input[name="search"]').val('<?=$qBuscar?>');
  $('.gsc-search-button .gsc-search-button-v2').click();
  }, 1000);
</script>
</body>
</html>