How to simulate/trigger keydown of tab in JavaScript?

Question

I'm trying to trigger a keydown of the tab key in JavaScript.

Scenario: 2 HTML input elements. Initially focus is on the 1st input, then wait 3 seconds, then simulate pressing of the tab key, which should set focus to the 2nd input.

Issue: Dispatching a tab keydown event does nothing.

Fiddles:

• Using KeyboardEvent & dispatchEvent - http://jsfiddle.net/dH9ZE/
• Using simulant.js - http://jsfiddle.net/3E5dB/

I am after a JavaScript solution. No jQuery thanks.

Fiddle example using simulant.js below:

HTML:

<input id="first">
<input id="second">
<p>Dispatching Tab keydown event in 3 seconds... <span id="done" style="color:red"></span></p>

JavaScript:

//simulates keydown of the tab key
function simulateTab() {
    var TAB_KEY = 9;    
    simulant.fire(document, 'keydown', { keyCode: TAB_KEY });
}

//focus 'first' input
document.getElementById('first').focus();

//focus 'second' input after 3 seconds
setTimeout(function(){
    simulateTab();
    document.getElementById('done').innerHTML = 'Done!';
}, 3000);