When on a Stack Exchange network review tab, periodically checks whether there is a review available.

loadReview.user.js

// ==UserScript==
// @name         Load review
// @namespace    https://gist.github.com/mogsdad/50c5a3e9686cf0a8867f
// @version      1.2
// @description  When on a Stack Exchange network review tab, periodically checks whether there is a review available.
// @author       David Bingham (Mogsdad)
// @include      /^https?://(meta\.)?(stackoverflow|stackexchange|serverfault|superuser|askubuntu|stackapps)\.com/review/*/
// @grant        none
// ==/UserScript==

(function () {
  "use strict";
  var debugging = false;      // Set true to enable logs
  var interval = 30 * 1000;   // reload interval, ms
  var waiting = "Waiting..."  // String to display when waiting for a post
  
  var title = document.title;
  debug(title);

  // Set to call function after all ajax loads are complete
  $(document).ajaxStop(loadReview);

  function loadReview() {
    debug('starting');
    var re = /^(\/review\/[^\/]+)\/.*$/; // Remove tab or post ID from end of URL
    var path = window.location.pathname.replace(re, '$1');
    debug(path);
    var anchor = 'a[href="' + path + '"]';
    debug(anchor);
    var revTab = $(anchor);
    debug(revTab.length);
    var onRevTab = revTab.hasClass('youarehere');
    debug(onRevTab);
    if (onRevTab) {
      if ($('.review-content').is(':empty')
          && $('.review-instructions:contains("Thank you")').length === 0
          && $('.review-instructions:contains("You have no more")').length === 0
          && $('.review-instructions:contains("There are no items")').length === 0) {
        debug('no post');
        document.title = waiting;
        var timeoutID = setTimeout('$(\'.youarehere\')[0].click();', interval);
        debug('timer ID: ' + timeoutID +' interval:' + interval);
      } 
      else {
        if (document.title === waiting) document.title = title;
        debug('have post or done reviewing');
      }
    }
  }
  function debug(msg) {
    if (debugging) console.log('loadReview: '+msg);
  }
})();