This script clicks the "Show New Tweets" button on Twitter whenever it available, allowing you watch your stream without interaction.

autoRefreshNewTweets.js

var autoRefreshNewTweets = function () {
    var newTweetsBar = document.getElementsByClassName('new-tweets-bar');
    if ('undefined' !== typeof newTweetsBar[0]) {
        newTweetsBar[0].click();
    }
    setTimeout(autoRefreshNewTweets, 1000);
}
autoRefreshNewTweets();

// Reload the entire page every hour, basically flushing the page so it doesn't become too "heavy"
setTimeout(function () {window.document.location.reload();}, 3600000);