Im afraid that the SearchSelectLister, SearchLinkLister, SearchRadioLister do not listen to the TimeRangePicker's time range. While they all do have a param called 'applyOuterIntentionsToInternalSearch' which makes them pay attention to the 'intentions' coming down from above, there is no corresponding switch that provides the same thing for time ranges.
This has been known internally for a while at least on some level but i think it may have been lost because i cant find anything filed around it.
For now I recommend trying to get by hardwiring the timerange using the 'earliest' param and the 'latest' param on the module.
Another more heavyweight way is to use a 'switcher' module like PulldownSwitcher, and beneath that switcher write basically the same UI N different ways, each with a different hardcoded timerange. There's an example or two of how to use switcher modules in the ui_examples app.
And its possible to make a StaticSelect module that outputs time terms, and use a stringreplace intention to write the selected time term into the search string itself. This approach could also be made to work but it has a number of drawbacks.
