How should I define a MENU_LOCAL_ACTION menu item, and which is the involved page callback?
Router items can inherit properties from parent paths.

In this case, the page callback is inherited from the 'admin/people' path:

$items['admin/people'] = array(
  'title' =&gt; 'People', 
  'description' =&gt; 'Manage user accounts, roles, and permissions.', 
  'page callback' =&gt; 'user_admin', 
  'page arguments' =&gt; array('list'), 
  'access arguments' =&gt; array('administer users'), 
  'position' =&gt; 'left', 
  'weight' =&gt; -4, 
  'file' =&gt; 'user.admin.inc',
);


The fact that the menu item is a MENU_LOCAL_ACTION doesn't actually come into it, the same is true of any type of item.

So if you define a router item like this:

$items['mymodule/path'] = array(
  'title' =&gt; 'Something',
  'page callback' =&gt; 'mymodule_page_callback',
  'access callback' =&gt; 'mymodule_access_callback',
);


And then define one like this:

$items['mymodule/path/sub-path'] = array(
  'title' =&gt; 'Something',
  'type' =&gt; MENU_LOCAL_ACTION,
  'access callback' =&gt; 'mymodule_access_callback',
);


The page callback will be inherited from the 'parent' item.