gistfile1.js

//Place your logic in some js function, e.g. check_current_user:
  <script>
    function check_current_user() {
       BTSW.current_user(function(user){
         // replace the line below with your logic, e.g. if user then show or hide something
         console.log("---- check_current_user : ", user);
       })
    }
  </script>

//Then add script.onload = check_current_user to the widget's code:
<script>
var BTSW = window.BTSW || {};
(function () {
var script = document.createElement('script');
script.type = 'text/javascript';
script.async = true;
script.src = 'https://faucet.bitshares.org/widgets/1/w.js?ref='+encodeURIComponent(document.referrer);
script.onload = check_current_user;
var entry = document.getElementsByTagName('script')[0];
entry.parentNode.insertBefore(script, entry);
}());
</script>