How do I find out which (page) template file my custom child post is looking for?

If think you were using the wrong filter, please try using ‘single_template’.

I assume you have created a plugin to create your custom post type. In the plugin folder you have a “templates” folder where you put the single page template called “palaver_single.php”.

function palaver_single_mapping($single) {

global $post;

    if ( $post->post_type == 'palaver' ) {
        if ( file_exists( plugin_dir_path( __FILE__ ) . '/templates/palaver_single.php' ) ) {
            return plugin_dir_path( __FILE__ ) . '/templates/palaver_single.php';
        }
    }

    return $single;
}
add_filter( 'single_template', 'palaver_single_mapping' );

So if a single palaver post is viewed, the template file inside the templates folder will be used.