What files will Drupal poll for hooks by default? I tried implementing hook_menu() in an foo.admin.inc file for reasons that aren't important, and discovered that hooks are not checked in said file. However, in the past, I have seen include files with hooks defined in them (e.g. rules.inc), so I was wondering what the default core rule is for this, and how one can specify files outside of the defaults. Does extending where hooks can be checked have a nice Drupal way of doing this, or have module developers used PHP to achieve this end?
An include file will be scanned if the hook is within a group. For example, the rules module defines a group called 'rules' and so Drupal will scan the file foo.rules.inc for implementations of rules hooks.

The hook where groups are defined is hook_hook_info.
See: https://api.drupal.org/api/drupal/modules!system!system.api.php/function/hook_hook_info/7

Also, look at the function module_implements that finds modules implementing a hook: https://api.drupal.org/api/drupal/includes!module.inc/function/module_implements/7