JSFiddle - React, Tailwind, and code Playground

HTML

<input type="text" value="" title="Target Date" />
<input type="submit" name="diidIOSaveItem" style="display: none;" /><br /><br />

<input type="submit" id="setvalue" value="Set a value" />

JavaScript

$("input[title='Target Date']").bind('change keyup',function(){
  $("input[name$='diidIOSaveItem']").toggle($(this).val()!='');
});

$("#setvalue").click(function(){  
  $("input[title='Target Date']").val("hello");
  $("input[title='Target Date']").change();
});