Create a Dropdown Selector and Redirect for a Custom Taxonomy in WordPress?

Never mind!

I managed to come up with a solution.

function insert_location(){
    ob_start();
?>
    <select name="location" id="location" class="postform">
        <?php
           $tax_terms = get_terms('location', array('hide_empty' => '0'));      
           foreach ( $tax_terms as $tax_term ):  
              echo '<option value="-1">Select a Location</option><option class="level-0" value="'.get_term_link($tax_term).'">'.$tax_term->name.'</option>';   
           endforeach;
        ?>
    </select> 
<script type="text/javascript">
    
/* <![CDATA[ */
(function() {
    var dropdown = document.getElementById( "location" );
    function onLocChange() {
        if ( dropdown.options[ dropdown.selectedIndex ].value != "-1" ) {
            window.location.href = dropdown.options[ dropdown.selectedIndex ].value;
        }
    }
    dropdown.onchange = onLocChange;
})();
/* ]]> */
</script>
<?php
    return ob_get_clean();
}
add_shortcode('location_filter','insert_location');

Instead of using the Term ID, I have replaced it with

.get_term_link($tax_term).

And rather than submitting with a form, I have chosen to use the following line of code.

window.location.href = dropdown.options[ dropdown.selectedIndex ].value;