$args = array(
  'post_type' => 'auction_dates',
  'paged' => $paged,
  'posts_per_page' => 1,
  'meta_key'    => 'date_of_auction',
  'orderby' => 'meta_value_num',
  'order' => 'ASC');

$previous_adjacent_post = get_adjacent_post(true,'',true, 'product_cat');
$next_adjacent_post = get_adjacent_post(true,'',false, 'product_cat');

if(is_a($previous_adjacent_post, 'WP_Post')){
     $previous_link = get_permalink($previous_adjacent_post->ID);
     $previous_title = $previous_adjacent_post->post_title;
}
if(is_a($next_adjacent_post, 'WP_Post')){
     $next_link = get_permalink($next_adjacent_post->ID);
     $next_title = $next_adjacent_post->post_title;
}

<?php next_post_link_plus( array('in_same_meta' => 'publisher') ); ?>

function get_adjacent_posts($args) {
    global $post;

    $all_posts = get_posts($args);
    $len = count($all_posts);
    $np = null;
    $cp = $post;
    $pp = null;

    if ($len > 1) {
        for ($i=0; $i < $len; $i++) {
            if ($all_posts[$i]->ID === $cp->ID) {
                if (array_key_exists($i-1, $all_posts)) {
                    $pp = $all_posts[$i-1];
                } else {
                    $new_key = $len-1;
                    $pp = $all_posts[$new_key];

                    while ($pp->ID === $cp->ID) {
                        $new_key -= 1;
                        $pp = $all_posts[$new_key];
                    }
                }

                if (array_key_exists($i+1, $all_posts)) {
                    $np = $all_posts[$i+1];
                } else {
                    $new_key = 0;
                    $np = $all_posts[$new_key];

                    while ($pp->ID === $cp->ID) {
                        $new_key += 1;
                        $np = $all_posts[$new_key];
                    }
                }

                break;
            }
        }
    }

    return array('next' => $np, 'prev' => $pp);
}

$args = array(
    'post_type' => 'custom_post_type',
    'posts_per_page' => -1,
    'order' => 'ASC',
    'orderby' => 'title'
);

$adjacent = get_adjacent_posts($args);

$next_title = $adjacent['next']->post_title;
$next_image = get_the_post_thumbnail_url($adjacent['next']->ID, 'square');
$next_url = get_permalink($adjacent['next']);

$prev_title = $adjacent['prev']->post_title;
$prev_image = get_the_post_thumbnail_url($adjacent['next']->ID, 'square');
$prev_url = get_permalink($adjacent['prev']);