Hi Luke, the link is always going to exist if there are adjacent events (an earlier and later dated event) to the current event. When you get to the latest event post you will not see a next event link and vise versa for the earliest event.
The tribe_previous_event_link automatically echo’s the value if it exists. I searched for this function in the code and found that within it contains a call to get_event_link which you should be able to use as a conditional check.
Try something like this:
global $post;
$tribe_ecp = TribeEvents::instance();
$next = $tribe_ecp->get_event_link($post,'next',$anchor);
$prev = $tribe_ecp->get_event_link($post,'previous',$anchor);
if($next != '') {
echo 'its not empty!';
} else {
echo 'its empty!';
}