Hook the “add_meta_boxes_{$post_type}” action. There’s another one for all post types, but this dynamic one is usually preferable.
Use remove_meta_box() to remove the one WP assigns for your taxonomy. Examine the values in the global array $wp_meta_boxes to determine the ID for your taxonomy. It should be something like “{$your-taxonomy}div”. Add another meta box using the ID form “tagsdiv-{$your-taxonomy}”. In the arguments for add_meta_box(), include “post_tags_meta_box” as the callback, null for $screen, ‘side’ for $context, ‘core’ for $priority, and in the $callback_args array include 'taxonomy'=> $your-taxonomy,
as an element.
This replaces the default with the one used for non-hierarchical taxonomies. This concept is untested, but it ought to be valid.