Вроде работает
<!doctype html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Document</title>
<script src="http://code.jquery.com/jquery-latest.min.js"></script>
</head>
<body>
<button>bla-bla</button>
<script>
var el = document.getElementsByTagName('button')[0];
el.addEventListener('click', function() {
alert('Click');
});
var timer = setInterval(function() {
var now = new Date();
var date = new Date(now.getFullYear(), now.getMonth(), now.getDate(), 12, 0);
if(now.toLocaleString() == date.toLocaleString()) {
el.click();
console.log('yes');
}
}, 1000);
</script>
</body>
</html>