Multi level archive

This is a direction. Not tested but you have an idea.

<?php
// get current term
$term = get_term_by( 'slug', get_query_var('term'), get_query_var('taxonomy') );
// get parent term
$parent = get_term($term->parent, get_query_var('taxonomy') );
// get children
$children = get_term_children($term->term_id, get_query_var('taxonomy'));

$taxonomy = 'business-types';

if ( empty($parent->term_id) ) {
    echo '<a href="' . esc_url( get_term_link( $term ) ) . '">' . $term->name . '</a><br />';
    $args = array(
        'child_of' => $term->term_id,
        'taxonomy' => $term->taxonomy,
        'hide_empty' => 1,
        'hierarchical' => true,
        'depth'  => 1
    );

    echo '<ul>';
    wp_list_categories($args);
    echo '</ul>';

// Subcategories
} elseif ($parent->term_id && sizeof($children) == 0) {
    $subterm = get_queried_object();
    // $parents = $subterm->parent; // May be will be useful in the future
    // $term_id = $subterm->term_id; //May be will be useful in the future
    echo '<a href="' . esc_url( get_term_link( $term ) ) . '">' . $subterm->name . '</a><br />';
    $args = array (
        'taxonomy'  => $taxonomy,
        'pad_counts'=> 0,
        'title_li'  => '',
        'child_of'  => $subterm->parent,
    );

    echo '<ul>';
    wp_list_categories($args);
    echo '</ul>';
}

For Parent Term listing you have to go here.