diff --git a/Library/Homebrew/utils/github/api.rb b/Library/Homebrew/utils/github/api.rb
index 55ef244855..10b59ff8a4 100644
--- a/Library/Homebrew/utils/github/api.rb
+++ b/Library/Homebrew/utils/github/api.rb
@@ -50,8 +50,7 @@ module GitHub
         @github_message = github_message
         super <<~EOS
           GitHub API Error: #{github_message}
-          Try again in #{pretty_ratelimit_reset(reset)}, or:
-          #{CREATE_GITHUB_PAT_MESSAGE}
+          Try again in #{pretty_ratelimit_reset(reset)}#{!API.credentials ? ", or:\n" + CREATE_GITHUB_PAT_MESSAGE : ""}
         EOS
       end