Hey Patrick,
You can try and use the following code for the pagination link.
<?php next_posts_link( 'Older Posts', $past_query->max_num_pages ); ?><?php previous_posts_link( 'Newer posts' ); ?>
This page should give you an idea about how to go about it: https://codex.wordpress.org/Function_Reference/next_posts_link#Usage_when_querying_the_loop_with_WP_Query.
I hope this helps.
