I don't think you need that. Why would you want search engine friendly search results URL? As far I understand SEO, you don't want your search results to appear as results on Google, Bing, etc.
And in my opinion www.example.com/search?q=test
is much more "friendly" than www.example.com/page2/test
because it is more obvious what it is. (Search results page.)
But, maybe I'm overlooking something, OK.
There are probably much better ways, but I think this should work also:
<script>
var searchFromURL = function() {
var element = google.search.cse.element.getElement('searchfromurlgname');
// you can echo query with PHP or get it from window.location
element.execute( window.location.pathname.replace('/page2/', '') );
};
var myCallback = function() {
if (document.readyState == 'complete') {
searchFromURL();
} else {
google.setOnLoadCallback(searchFromURL, true);
}
};
window.__gcse = {
callback: myCallback
};
(function() {
var cx = '013315504628135767172:d6shbtxu-uo';
// Insert your own Custom Search engine ID here
var gcse = document.createElement('script'); gcse.type = 'text/javascript';
gcse.async = true;
gcse.src = (document.location.protocol == 'https' ? 'https:' : 'http:') +
'//www.google.com/cse/cse.js?cx=' + cx;
var s = document.getElementsByTagName('script')[0];
s.parentNode.insertBefore(gcse, s);
})();
</script>
<gcse:searchbox-only></gcse:searchbox-only>
<gcse:searchresults-only gname="searchfromurlgname"></gcse:searchresults-only>
<!-- switch CSE layout to "two page" -->
https://developers.google.com/custom-search/docs/element#tagparams