It’s not a module. But the error message does look like it is trying for the council controller except that in the error log it looks to be trying to get the right controller
The URL is as Gii suggested for me /council/president
The Gii help popup suggests that entering admin/user for the controller will generate admin/UserController.php and that is exactly what it does for council/president Gii makes a new folder protected/controllers/council/PresidentController.php
The Controller documentation section 2 suggests the same thing
If the ID is in the format 'path/to/xyz', the controller class name is assumed to be XyzController and the corresponding class file is protected/controllers/path/to/XyzController.php. For example, a controller ID admin/user would be mapped to the controller class UserController and the class file protected/controllers/admin/UserController.php. If the class file does not exist, a 404 CHttpException will be raised.
which if it was doing as you suggest would mean that admin/UserController would try to use the AdminController at least that is how I read the docs to mean.
Looks like I did not understand.
I tried a different approach. first I created banana/president from Gii and it worked as expected with a controller at controllers/banana/PresidentController.php
next with Gii created controller banana which works but now banana/president gives the action not found error so I guess you can’t nest controllers like that.