Assuming you have done something like this (note time_tok1
😞
<fieldset autoRun="true" submitButton="false">
<input type="time" token="time_tok1" searchWhenChanged="true">
<label>First TimePicker</label>
<default>Last 24 hours</default>
</input>
</fieldset>
Then change your panel like this:
<search>
<query>My Search Here</query>
<earliest>$time_tok1.earliest$</earliest>
<latest>$time_tok1.latest$</latest>
</search>