I want to use the search widget to do incremental search, like it does in most OS X apps. This requires updating every time the search widget changes. onKeyUp catches most things except clicking the (x) button, which only seems to fire events _before_ it clears the widget, not _after_, so it's pretty hard to detect.
The 'search' event is fired when the close (x) button is clicked (so setting the 'onsearch' attribute to a handler should catch it). The event is fired after the value is reset. I verified this in both shipping Safari and TOT WebKit.