Linking from CPT page to taxonomy.php

You can create a taxonomy-people_categories.php or a more general taxonomy.php (which will display all your taxonomies in this category – excluding post categories) – please see Taxonomy Templates / Template Hierarchy.

As far as a what you need to display your posts, once you have the taxonomy-people_categories.php created you can just run the normal WordPress loop:

<?php if(have_posts()) : ?>
    <?php while(have_posts()) : ?>
        <?php the_title(); ?>
    <?php endwhile; ?>
<?php endif; ?>

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