When paginating a Page with the tag, how can the 2nd and subsequent page styles be customised?

WordPress already adds classes to the body for you to handle this, as long as your theme correctly uses the body_class template tag.

On the 2nd page of Page, your body will have these additional classes: paged, paged-2 & page-paged-2, so you can see that you can make changes to styles to suit:

body.page {
    background: black;
    color: white;
}

body.paged {
    background: green;
    color: red;
}

Core achieves this with this logic:

global $wp_query;

$page = $wp_query->get( 'page' );

    if ( ! $page || $page < 2 )
        $page = $wp_query->get( 'paged' );

    if ( $page && $page > 1 && ! is_404() ) {
        $classes[] = 'paged-' . $page;

        if ( is_single() )
            $classes[] = 'single-paged-' . $page;
        elseif ( is_page() )
            $classes[] = 'page-paged-' . $page;
        elseif ( is_category() )
            $classes[] = 'category-paged-' . $page;
        elseif ( is_tag() )
            $classes[] = 'tag-paged-' . $page;
        elseif ( is_date() )
            $classes[] = 'date-paged-' . $page;
        elseif ( is_author() )
            $classes[] = 'author-paged-' . $page;
        elseif ( is_search() )
            $classes[] = 'search-paged-' . $page;
        elseif ( is_post_type_archive() )
            $classes[] = 'post-type-paged-' . $page;
}

You could adapt this logic within your templates if you wanted to use different HTML on the first & subsequent pages.

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