Hi Nick,
Maybe the editor you're using strips out HTML tags so it causes issue. You can try disabling default editor via Global Configuration first and add content again.
Here is default output of this module in topbar-l position:
<ul>
<li>
<a href="tel:+000" title="(480) 555-0103">(480) 555-0103</a>
</li>
<li>
<a href="mailto:hello@phio.com" title="hello@phio.com">hello@phio.com</a>
</li>
</ul>