wp-menu ‘automatically add custom taxonomy terms’ like it does for pages?

I’ve added a new wp_menu to my sidebar on a custom post-type page. The wp_menu displays a list of a custom taxonomies terms.

I see that wp_menu has the checkbox to automatically add new top level pages to the menu.

Is there a function that I can add to my theme that will allow it to automatically add terms from a specific taxonomy?

*second question:

this menu is displayed on the sidebar of my custom post-type. When on the post-type-single.php template is there also an easy way to highlight the currently active term/terms?

-I found one post on this same question here, but the solution provided was to hardcode all the terms and I do not want to do that. Would rather it be automated.

thanks