Take a custom taxonomy value and save as a standard Product Tag

Got it worked out, working code as follows:

function action_save_product_data( $post_id ) {
  if ( 'product' !== $post->post_type ) {
    $terms = wp_get_post_terms( $post_id, 'product_brand', array( 'fields' => 'all' ) );
    if ( $terms ) {
      $prod_brand = $terms[0]->slug;
      wp_set_object_terms( $post_id, $prod_brand, 'product_tag', true );
    }
  }
}