Query with no terms uses index.php template instead of archive.php

You could filter template_include:

add_filter( 'template_include', 'wpse_97347_force_archive' );

function wpse_97347_force_archive( $template )
{
    if ( isset ( $_GET['makemodel'] ) && empty ( $_GET['makemodel'] ) )
        return get_archive_template();

    return $template;
}

Not tested.