Possible to have one template call different sidebars for different pages?

If you’re using static pages, try using is_page() for your conditionals. Let’s assume your static pages have slugs, “customers”, “vendors”, and “services”:

<?php
if ( is_page( 'customers' ) :
    get_sidebar('customer');
elseif ( is_page( 'vendors' ) ) :
    get_sidebar('vendors');
elseif ( is_page( 'services' ) ) :
    get_sidebar('services');
else :
    get_sidebar();
endif;
?>

But I agree with @markratledge that you’re probably better-served using a single sidebar, and Widget Logic.