Entity translation translate tab doesn't work on custom entity

Thank you Nickolas! Yeah, i tested it out and there are still problems. As I said probably something is wrong with 'base path' I use. In Commerce Product i see that during debugging Entity object is passed to edit form, while in my code it passes entity id, this is why i can't see entity-entry values. But i don't know how to fix it yet, unfortunately.

I also think that

'base path' => 'admin/custom_entities/manage/%custom_entity',
'path wildcard' => '%',

should match, like

'base path' => 'admin/custom_entities/manage/%',
'path wildcard' => '%',

This is why i specify 'path wildcard' explicitly, to let system know that i use custom path wildcard. Probably this is also a point where problem happens. Still don't know why normal '%custom_entity' doesn't work. Actually translate tab only appears in each entity-entry (where it's needed) when i use that latest piece of code above:

'base path' => 'admin/custom_entities/manage/%',
'path wildcard' => '%',

but as i said, in that case only entity id instead of entity object is passed to translate-edit-trasnlation form which turns into empty entity-entry values. So this makes me think i need to adapt '%custom_entity' because it somehow says system to pass entity object instead of entity-id param like '3'. Probably another question is which mechanism causes param-to-entity-object conversion.

CRUD works fine on custom-entity-entries itself, but if i use:

	'base path' => 'admin/custom_entities/manage/%custom_entity',
	'path wildcard' => '%custom_entity',

or as you mentioned, we can simply specify 'base path' without 'path wildcard' since entity id is as expected - '%custom_entity':

	'base path' => 'admin/custom_entities/manage/%custom_entity'	

However, in that case 'TRANSLATE' tab appears inside 'Custom entitys' list, instead of inside inside each custom-entity-entry:

This initially was a problem and i started to try different combinations with base path like 'admin/custom_entities/manage/%' after which 'TRANSLATE' tab appears where it's needed, but still doesn't work correctly.

No, it unfortunately still displays 'TRANSLATE' tab on `custom-entitys` list page (as far as i know all other paths are based on 'base path' so we can omit it in configuration array). Maybe explicit hook_menu() entry is needed to make everything work, but i'm not sure. I'll try to re-investigate Commerce Product module and it's Commerce Product UI companion module.

Btw i'm surprised that custom entities translation is such an uncommon topic. I thought a lot of people need it or is there another way to store multilingual content in custom db table? I tried nodes for this but performance is so low that it takes a lot to load nodes i need on single page request, so i wanted to create custom entity instead (since i need custom db table and admin UI), but obviously it is troublesome at the moment since there are no good basic examples..

Didn't fully test it yet because I'm heavily into Drupal 8 now, but this is what I did and now tab content appears correctly for both add and edit forms. Just needed to append these 2 functions inside test.module:

/**
 * Loads a custom-entity by ID.
 */
function custom_entity_load($entity_id) {
  if (empty($entity_id)) {
    return FALSE;
  }

  $entities = custom_entity_load_multiple(array($entity_id), array());
  return $entities ? reset($entities) : FALSE;
}

/**
 * Loads multiple custom-entities by ID or based on a set of matching conditions.
 *
 * @see entity_load()
 *
 * @param $entity_ids
 *   An array of entity IDs.
 * @param $conditions
 *   An array of conditions on the {custom_entity} table in the form
 *     'field' => $value.
 * @param $reset
 *   Whether to reset the internal custom-entity loading cache.
 *
 * @return
 *   An array of custom-entity objects indexed by entity_id.
 */
function custom_entity_load_multiple($entity_ids = array(), $conditions = array(), $reset = FALSE) {
  if (empty($entity_ids) && empty($conditions)) {
    return array();
  }

  return entity_load('custom_entity', $entity_ids, $conditions, $reset);
}

I took it from commerce product module and adapted to my custom-entity.

How did I came up to this? This is excerpt from Pro Drupal 7 Development book:

$items['user/%user_uid_only_optional'] = array(
  'title' => 'My account',
  'title callback' => 'user_page_title',
  'title arguments' => array(1),
  'page callback' => 'user_view_page',
  'page arguments' => array(1),
  'access callback' => 'user_view_access',
  'access arguments' => array(1),
  'weight' => -10,
  'menu_name' => 'user-menu',
);

When Drupal creates the menu using user/%user_uid_only_optional, it replaces the
%user_uid_only_optional using the process as described below:

1. In the second segment, match the string after the % and before the next possible slash. In this case, the string would be user_uid_optional.
2. Append _load to the string to generate the name of a function. In this case, the
   name of the function is user_uid_optional_load.
3. Call the function and pass it, as a parameter, the value of the wildcard in the
   Drupal path. So if the URL is http://example.com/?q=user/2375, the Drupal
   path is user/2375, and the wildcard matches the second segment, which is
   2375. So a call is made to user_uid_optional_load('2375').
4. The result of this call is then used in place of the wildcard. So when the title
   callback is called with the title arguments of array(1), instead of passing part 1
   of the Drupal path (2375), we pass the result of the call to
   user_uid_optional_load('2375'), which is a user object. Think of it as a
   portion of the Drupal path being replaced by the object it represents.
5. Note that the page and access callbacks will also use the replacement object.
   So in the previous menu item, user_view_access() will be called for access and
   user_view() will be called to generate the page content, and both will be
   passed the user object for user 2375.

So this is why i had (for example) '1' (integer value) passed as $entity_object instead of actual object. So to fix this you need to use _load function as explained in the steps above.

Hope it will help to someone, since i spent several days trying to figure everything out :)