Customizer related question

you can define the conditional display on definition in PHP with that in the arguments array of footer_tauthor

$wp_customize->add_control( new WP_Customize_Control( $wp_customize, 'footer_tauthor',
    array(
        // other args ...
        "active_callback" => function ($control) {
            return $control->manager->get_setting("checkboxSettingName")->value();
        },
    ) 
) );