That is "Desktop" and "Mobile" links are not from Select Markup modules? Are they embedded as custom HTML module?

They are menu items assigned as external links each with link: index.php/?device=desktop AND index.php/?device=xhtml. The index.php, declaration ensures that the user, regardless of what page they are on can switch between desktop and mobile without being redirected away from the page they are on.

The menu items are setup on the standard menu module which is assigned to position <jdoc:include type="modules" name="website-version" style="none" />

Thanks,

Morgan

Most likely it is main point. Menu items are passed through SEF, and MJ affects SEF to add device=[mode] parameter (if necessary). I'd transform it to custom html module.

We will try to fix it in next MJ release (to don't change device parameter in URL if it is presented).

If that is the case...why would both links work on the mobile device? They are still passing through the SEF in order to be rendered in both cases?

Because of "device" parameter is changed in "forced" mode only and there are some differences in work in mobile and desktop modes.