Comment Email Notification for CPT Comments

I have figured it out. There were a bunch of issues with the existing code.

The code wasn’t getting $author_email appropriately which was causing it to fail and causing wp_mail() not to fire.

add_action('comment_post', 'comment_email_notification', 11, 2);

function comment_email_notification($comment_ID, $comment_approved) {
    $post_type = get_post_type();
    if ($post_type !== 'jobs') {
        return;
    }

    $comment = get_comment($comment_ID);
    $post_ID = $comment->comment_post_ID;
    $author_ID = get_post_field( 'post_author', $post_ID );
    $author_email = get_the_author_meta( 'user_email', $author_ID );
    if (isset($author_email) && is_email($author_email)) {
        $message="New comment on <a href="" . get_permalink($post_ID) . '">' .
            get_the_title($postid) . '</a>';

        add_filter('wp_mail_content_type',
                   create_function('', 'return "text/html";'));

        wp_mail($author_email, 'New Comment', $message);
    }
}