Allow UI to choose which search module is default tab

Seems that site search box do not take search type into account:

function search_box_form_submit($form, &$form_state) {
  $form_id = $form['form_id']['#value'];
  $form_state['redirect'] = 'search/node/'. trim($form_state['values'][$form_id]);
}

It is always passing 'search/node/' as a default search type. I want to have my search type to be used as default instead of node. Maybe it would be better to implement any hidden parameter in form showing the search type? If it is not present search_box_form_submit will use 'search/node/' as type. This would provide backward comportability.

Thanks,
Grigory