I have a JSF input text component which has an id of search. In the generated HTML output it looks like this j_idt17:search, but the number 1
Give the JSF component which generated the HTML element with id="j_idt17" a fixed ID. In this particular case, it's likely the HTML input element's parent <form> element which is generated by the JSF <h:form> component.
So, this should do:
<h:form id="form">
This way the ID of the generated HTML <input> element will become form:search.