Second check for github repos as private homepages

Library/Homebrew/cask/audit.rb

@@ -716,7 +716,7 @@ module Cask
 
       return unless cask.homepage
 
-      validate_url_for_https_availability(cask.homepage, "homepage URL", cask.token, cask.tap,
+      validate_url_for_https_availability(cask.homepage, SharedAudits::URL_TYPE_HOMEPAGE, cask.token, cask.tap,
                                           user_agents:   [:browser, :default],
                                           check_content: true,
                                           strict:        strict?)

Library/Homebrew/formula_auditor.rb

@@ -498,7 +498,7 @@ module Homebrew
       end
 
       if (http_content_problem = curl_check_http_content(homepage,
-                                                         "homepage URL",
+                                                         SharedAudits::URL_TYPE_HOMEPAGE,
                                                          user_agents:       [:browser, :default],
                                                          check_content:     true,
                                                          strict:            @strict,

Library/Homebrew/utils/curl.rb

@@ -290,9 +290,27 @@ module Utils
           url_protected_by_cloudflare?(response) || url_protected_by_incapsula?(response)
         end
 
+        # https://github.com/Homebrew/brew/issues/13789
+        # If the `:homepage` of a formula is private, it will fail an `audit`
+        # since there's no way to specify a `strategy` with `using:` and
+        # Github does not authorize access to the web ui using token
+        #
+        # Strategy:
+        # If the `:homepage` 404s, it's a github link, and we have a token--
+        # check the API for the repository existing (which does use tokens)
+        repo_details = url.match(%r{https?://github\.com/(?<user>[^/]+)/(?<repo>[^/]+)/?.*})
+        check_github_api = url_type == SharedAudits::URL_TYPE_HOMEPAGE &&
+                           details[:status_code] == "404" &&
+                           repo_details &&
+                           Homebrew::EnvConfig.github_api_token
+
+        unless check_github_api
           return "The #{url_type} #{url} is not reachable (HTTP status code #{details[:status_code]})"
         end
 
+        "Unable to find homepage" if SharedAudits.github_repo_data(repo_details[:user], repo_details[:repo]).nil?
+      end
+
       if url.start_with?("https://") && Homebrew::EnvConfig.no_insecure_redirect? &&
          (details[:final_url].present? && !details[:final_url].start_with?("https://"))
         return "The #{url_type} #{url} redirects back to HTTP"

Library/Homebrew/utils/shared_audits.rb

@@ -10,6 +10,8 @@ module SharedAudits
   include Utils::Curl
   extend Utils::Curl
 
+  URL_TYPE_HOMEPAGE = "homepage URL"
+
   module_function
 
   def github_repo_data(user, repo)