Hi
I tested your code in Js.do you forgotten a quote. I added in only the phone link work and launch my skype. I put a real email address to see if it open my email or outlook but it does nothing.
<html>
<body>
<ul data-role="listview">
<li>
option one<br />
<a href="mailto:girlfridayz@girlfridayz.com" data-rel="external">sample@email.com</a><br />
<a href="tel:1231231234" data-rel="external">123-123-1234</a>
</li>
<li>
option two<br />
<div onclick="window.location.href= 'mailto:girlfridayz@girlfridayz.com';">sample@email.com</div>
<div onclick="window.location.href = 'tel:1231231234';">123-123-1234</div>
</li>
</ul>
</body>