In the profile one can 'find all postings' of the user.
This returns all links, amongst the results.
Within the class search.class.php events are handled as author_less. Links are too.
Change search.class.php to have this :
function _searchLinks()
{
global $LANG09, $_CONF, $_TABLES;
// Build SQL
if (($this->_type == 'links') OR
(($this->_type == 'all') AND empty($this->_author))) {
Refer to _searchEvents() and see the difference.