I could not find a way to do this using parameters so I changed (kluged) the supplied code. If you do this you will have to reapply the change when a new version of MJ is installed.
edit
public_html/modules/mod_mj_markupchooser/mod_mj_markupchooser.php
change
//dont display for desktop user displayin desktop page
//forgedMarkup means user wanted to see some other version (like mobile wants desktop version)
$forgedMarkup = $mainframe->getUserState('mobilejoomla.forged_markup', false);
$desktopUserDesktopPage = ('yes' != $forgedMarkup) && ($markup == '');
to
# display for desktop users
//dont display for desktop user displaying desktop page
//forgedMarkup means user wanted to see some other version (like mobile wants desktop version)
$forgedMarkup = $mainframe->getUserState('mobilejoomla.forged_markup', false);
# $desktopUserDesktopPage = ('yes' != $forgedMarkup) && ($markup == '');
$desktopUserDesktopPage = false;
So you are effectively saying show the mobile version | standard version links regardless of whether the user is on a desktop or a mobile.