How to get term link that crosses different custom post types?

In my WordPress project, I have several different custom post types and they all share a common taxonomy. I am in the final stage of the project and now is time to link all custom post types using a sidebar widget. The problem I am having is that I don’t know the appropriate way to get the term link linked to the correct custom post type.

For example, I have custom post types: book, author, product; and a taxonomy: genre that includes a horror category.

I would like to be able to get link structure as such:

/book/genre/horror
/product/genre/horror
/author/genre/horror

When I do get_term_link('horror');, I get one of the term links, it seems that one of the custom post type has preference. How can I manage to get each term link corresponding to the correct custom post type?

Hard coding it is never a good idea, so I was wondering if there is a proper way to go about this. This is an old issue I am having, and have done a lot of searching for a solution but I didn’t find it. I come here as the last resort. Thanks.

This code display all posts of all categories of genre taxonomy for custom post type book. Now, For different custom post type (author, product ) you have to change Custom Post Type Name inside $arg of WP_Query(). You will get term link using get_term_link($catterm) function or you can use also get_the_term_list().

 $args = array(
            'number'     => $number,
            'hide_empty' => $hide_empty,
            'include'    => $ids
        );

        $custom_categories = get_terms( 'genre ', $args );

        foreach ( $custom_categories as $catterm){

            $arg = Array( 
            'post_type' => 'book',
            'posts_per_page' => '-1',
            'post_status' => 'publish',
            'tax_query' => Array( Array ( 
            'taxonomy' => 'genre ' ,
            'terms' => $catterm->term_id
            )) );

        $loop = new WP_Query( $arg ); 
        global $post;
        while ( $loop->have_posts() ) : $loop->the_post();
        ?>

        <div class="gallery-content">
        <div class="entry-content">

        <?php 
         echo '<li>' . get_the_title() . '</li>';
         echo '<li><a href="'.get_term_link($catterm).'">'.$catterm->name.'</a></li>';   
        ?>  

        </div>
        </div>

       <?php endwhile;
        }   
        ?>