This is a Firefox greasemonkey script that will "click" the new tweets bar after a set interval. It will not do so unless you're scrolled all the way to the top (so as not to distract by pushing content down).

twitter-auto-refresh.js

// ==UserScript==
// @name        Twitter Auto Click
// @namespace   http://www.github.com/cwgem/twitter-auto-click
// @description Click the new tweet banner unless the user is not scrolled to the top
// @include     https://twitter.com/
// @version     1
// @grant	none
// ==/UserScript==

function checkScrolledToTop() {
	var timeline = document.getElementById('timeline');
	var clientTop = timeline.getBoundingClientRect().top;
	var elementTop = timeline.offsetTop;
	return clientTop == elementTop;
}

window.setInterval( function() {
	var tweetbar = document.getElementsByClassName('new-tweets-bar');
	if (tweetbar.length != 0 && checkScrolledToTop()) {
		tweetbar[0].click();
	}
}, 5000);