I know this is an old question, but I was looking for the similar thing. Determine when the 'X' was clicked to clear the search box. None of the answers here helped me at all. One was close but also affected when the user hit the 'enter' button, it would fire the same result as clicking the 'X'.
I found this answer on another post and it works perfect for me and only fires when the user clears the search box.
$("input").bind("mouseup", function(e){
var $input = $(this),
oldValue = $input.val();
if (oldValue == "") return;
// When this event is fired after clicking on the clear button
// the value is not cleared yet. We have to wait for it.
setTimeout(function(){
var newValue = $input.val();
if (newValue == ""){
// capture the clear
$input.trigger("cleared");
}
}, 1);
});