How to add custom tax value if a custom checkbox field is checked?

I am trying to add custom tax value at woocommerce checkout page, but I want to show it only for specific country (Italy) and only if a custom checkbox field in the checkout page is checked.

I've already found this answer and I'm trying to adjust to my problem by editing the function conditional_custom_shipping_cost.

I do the following:

// Add a Custom checkbox field for shipping options (just for testing)
add_action( 'woocommerce_after_checkout_billing_form', 'custom_billing_checkbox_for_testing', 10, 1 );
function custom_billing_checkbox_for_testing( $checkout ) {
    $field_id = 'billing_ups_yn';

    // Get the checked state if exist
    $billing_ups = WC()->session->get('billing_ups' );
    if(empty($billing_ups))
        $billing_ups = $checkout->get_value( $field_id );

    // Add the custom checkout field (checkbox)
    woocommerce_form_field( $field_id, array(
        'type' => 'checkbox',
        'class' => array( 'form-row-wide' ),
        'label' => __('Billing UPS'),
    ), $billing_ups );
}

// function that gets the Ajax data
add_action( 'wp_ajax_woo_get_ajax_data', 'woo_get_ajax_data' );
add_action( 'wp_ajax_nopriv_woo_get_ajax_data', 'woo_get_ajax_data' );
function woo_get_ajax_data() {
    if ( $_POST['billing_ups'] == '1' ){
        WC()->session->set('billing_ups', '1' );
    } else {
        WC()->session->set('billing_ups', '0' );
    }
    echo json_encode( WC()->session->get('billing_ups' ) );
    die(); // Alway at the end (to avoid server error 500)
}

// Conditionally changing the shipping methods costs
add_filter( 'woocommerce_package_rates','conditional_custom_shipping_cost', 90, 2 );
function conditional_custom_shipping_cost( $rates, $cart ) {

    if ( WC()->session->get('billing_ups' ) == '1' ){
        if ( 'IT' != WC()->customer->get_shipping_country() ) return;

        $percent = 10;
        # $taxes = array_sum( $cart->taxes ); // <=== This is not used in your function

        // Calculation
        $surcharge = ( $cart->cart_contents_total + $cart->shipping_total ) * $percent / 100;

        // Add the fee (tax third argument disabled: false)
        $cart->add_fee( __( 'TAX', 'woocommerce')." ($percent%)", $surcharge, false );

    }
    return $rates;
}


// The Jquery script
add_action( 'wp_footer', 'custom_checkout_script' );
function custom_checkout_script() {
    ?>
    <script type="text/javascript">
        jQuery( function($){

            // update cart on delivery location checkbox option
            $('#billing_ups_yn_field input').change( function () {
                var checked = 0;
                if ( $('#billing_ups_yn').is(':checked') )
                    checked = 1;

                $.ajax({
                    type: 'POST',
                    url: wc_checkout_params.ajax_url,
                    data: {
                        'action': 'woo_get_ajax_data',
                        'billing_ups': checked,
                    },
                    success: function (result) {
                        $('body').trigger('update_checkout');
                        console.log('response: '+result); // just for testing
                    },
                    error: function(error){
                        console.log(error); // just for testing
                    }
                });
            });
        });
    </script>
    <?php
}

but I don't get the desired behavior (to work only if Italy selected)