I’ve managed to solve this using Javascript to ‘open’ the menu item when on the edit tags page in the plugin.
Relevant plugin PHP file
$screen = get_current_screen();
// Check we're only on the edit-tags page in the plugin
if ('edit-tags' === $screen->base && 'subscriber' === $screen->post_type) {
wp_enqueue_script( $this->plugin_slug . '-subscriber-edit-tags-script', plugins_url('assets/js/subscriber-edit-tags.js', __FILE__ ), array('jquery') );
}
subscriber-edit-tags.js (using jQuery)
(function ( $ ) {
/**
* File is called only when on edit tags under subscriber post type
*/
$('.toplevel_page_my_plugin')
.removeClass('wp-not-current-submenu')
.addClass('wp-has-current-submenu wp-menu-open')
.find('li').has('a[href*="edit-tags.php"]')
.addClass('current');
}(jQuery));