Both the domains and the sitesearch query parameters are currently protocol-relative. Google only allows naked hostnames or full hostnames with protocol.
We should probably be passing the canonical server there.
Dump:
<!-- SiteSearch Google -->
<form method="get" action="www.google.com/search" id="googlesearch">
<input type="hidden" name="domains" value="commons.wikimedia.org" />
<input type="hidden" name="num" value="50" />
<input type="hidden" name="ie" value="UTF-8" />
<input type="hidden" name="oe" value="UTF-8" />
<input type="text" name="q" size="31" maxlength="255" value="" />
<input type="submit" name="btnG" value="Search" />
<div>
<input type="radio" name="sitesearch" id="gwiki" value="//commons.wikimedia.org" checked="checked" /><label for="gwiki">Wikimedia Commons</label>
<input type="radio" name="sitesearch" id="gWWW" value="" /><label for="gWWW">WWW</label>
</div>
</form>
<!-- SiteSearch Google -->
Example url from submitting "test" with "Commons Wikimedia":
(which just searches the entire web)
Version: 1.19
Severity: normal