Eliminate BrowserProcess dependency from sign-in production code.

chrome/browser/signin/DEPS

 include_rules = [
   # Sign-in logic is being componentized (moved to //components, where
   # it won't depend back on //chrome), so we have restrictive DEPS and
   # are trying to get the list of temporarily-allowed (!-prefixed
   # rules) below to zero.
   "-chrome/common",
   "-chrome/browser",
   "+chrome/browser/signin",
 
   # TODO(joi): Get this list to zero.
-  "!chrome/browser/browser_process.h",
   "!chrome/browser/policy/cloud/user_policy_signin_service.h",
   "!chrome/browser/policy/cloud/user_policy_signin_service_factory.h",
   "!chrome/browser/profiles/profile.h",
   "!chrome/browser/profiles/profile_dependency_manager.h",
   "!chrome/browser/profiles/profile_info_cache.h",
   "!chrome/browser/profiles/profile_io_data.h",
   "!chrome/browser/profiles/profile_keyed_service.h",
   "!chrome/browser/profiles/profile_keyed_service_factory.h",
   "!chrome/browser/profiles/profile_manager.h",
   "!chrome/browser/sync/profile_sync_service.h",
@@ skipping 18 matching lines @@
   "!chrome/common/chrome_switches.h",
   "!chrome/common/chrome_version_info.h",
   "!chrome/common/extensions/extension_messages.h",
   "!chrome/common/pref_names.h",
   "!chrome/common/url_constants.h",
 ]
 
 specific_include_rules = {
   r".*_[a-z]*test\.cc": [
     # TODO(joi): Get this list to zero.
+    "!chrome/browser/browser_process.h",
     "!chrome/browser/prefs/browser_prefs.h",
     "!chrome/browser/sync/profile_sync_service_mock.h",
     "!chrome/browser/ui/browser.h",
     "!chrome/browser/ui/singleton_tabs.h",
     "!chrome/browser/ui/tabs/tab_strip_model.h",
     "!chrome/browser/ui/webui/sync_promo/sync_promo_ui.h",
   ],
 
   # These files are staying in //chrome so no need to limit.
-  r"chrome_signin_manager_delegate\.(h|cc)": [
+  r"(chrome_signin_manager_delegate|"
+  r"signin_names_io_thread.*|"
+  r"signin_manager_factory)"
+  r"\.(h|cc)": [
     "+chrome/browser",
     "+chrome/common",
   ],
 }