Most of the users don’t reach your second page on an archive page, so why not randomize your archive pages to get some hits for your older content.

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Here is a really simple trick to randomize your category and tag arhives.
Just open functions.php in your theme folder and put this code in

// Random ordered on category pages
function shailan_post_order( $query ) {
    if ( $query->is_archive ) {
        $query->set( 'orderby', 'rand' );
    }
}
add_action( 'pre_get_posts', 'shailan_post_order' );

Just save and upload it.

Visit any archive page (category, tag archives etc) and you will see your posts are randomized!

Hope you like this trick. Enjoy!