Time range picker is global if token is not defined.
Global time range picker is overridden by specific searches having declared time frames, either in xml or in the search string.
Being that you said all of your searches have those declared and the default is to include a token from the add input, It is an unused variable at the moment.
edit: I have the time range picker working in a global capacity by deleting the token="token" property and deleting any earilestTime and latestTime properties under and in a given search.
edit2: Below is for using the token.