I do not know, can already it was mentioned - I have not found.
In the file ajaxSearch.class.inc.php I see:
define ('OUTPUT_ID', ' < div id = "ajaxSearch_output" style = " opacity:0; filter:alpha (opacity=0);-moz-opacity:0.; " > </div > ');
But this code (filter:alpha (opacity=0);-moz-opacity:0.) is not valid CSS.
At the same time I can not correct it by template change without modification in the code, that it is inconvenient.
If this description of style is really necessary, maybe realize it by JavaScript (and it will not be present in HTML)?