Custom taxonomy widget in WordPress admin area

OK, so I’ve searched high and low and I have no idea how to do this, so let’s see if anyone on here can.

I have a custom taxonomy set up on a custom post type and the box it uses is the same as categories, except I wanted to make it easily searchable using a filter script and then also allow the user to only select one and not multiple.

I managed to get the search/filter working and to get it to display on the sidebar under the custom post type in the admin area and then I managed to hide the old box, but now I can’t seem to get the term that is associated to a specific “post”. So none of them is returning as selected once you update the page.

Code below:

function my_client_box() {

    add_meta_box(
        'clients_section',
        'The title',
        'clients_box',
        'cars',
        'side'
    );

}
add_action( 'add_meta_boxes', 'my_client_box' );

function clients_box() {

    echo '<div class="clients_out"><input id="livefilter-input" type="text" value="" placeholder="Search names" autocomplete="off">';
    echo '<div class="clients">';
    echo '<ul id="clientlist">';

    $terms = get_terms("client", 'orderby=name&order=ASC&hide_empty=0');
    $count = count($terms);
    if ( $count > 0 ){

        foreach ( $terms as $term ) {

            echo '<li><label><input type="radio" name="tax_input[client][]" value="' . $term->term_id . '"> <span>' . $term->name . '</span></label></li>';

        }

    }

    echo '</ul>';
    echo '</div>';
    echo '</div>';

    echo '
        <script src="' . get_bloginfo('template_directory') . '/js/jquery.liveFilter.js"></script>
        <script>
        jQuery(function($){
            $("#clientlist").liveFilter("#livefilter-input", "li", {
                filterChildSelector: "span"
            });
        });
        </script> 

    ';

}

So when I print_r the $term var there doesn’t seem to be any indication about if the specific name should be checked or not… how would I go about doing this?