The dynamic portion of the hook name, $action, refers to the action that brought the visitor to the login form.
Possible hook names include:
login_form_checkemaillogin_form_confirm_admin_emaillogin_form_confirmactionlogin_form_entered_recovery_modelogin_form_loginlogin_form_logoutlogin_form_lostpasswordlogin_form_postpasslogin_form_registerlogin_form_resetpasslogin_form_retrievepasswordlogin_form_rp