diff --git a/Library/Homebrew/brew.rb b/Library/Homebrew/brew.rb
index a6299cdc44..4edc7d5a2a 100644
--- a/Library/Homebrew/brew.rb
+++ b/Library/Homebrew/brew.rb
@@ -132,7 +132,9 @@ begin
     possible_tap = OFFICIAL_CMD_TAPS.find { |_, cmds| cmds.include?(cmd) }
     possible_tap = Tap.fetch(possible_tap.first) if possible_tap
 
-    odie "Unknown command: #{cmd}" if !possible_tap || possible_tap.installed?
+    if !possible_tap || possible_tap.installed? || Tap.untapped_official_taps.include?(possible_tap.name)
+      odie "Unknown command: #{cmd}"
+    end
 
     # Unset HOMEBREW_HELP to avoid confusing the tap
     with_env HOMEBREW_HELP: nil do
diff --git a/Library/Homebrew/cli/named_args.rb b/Library/Homebrew/cli/named_args.rb
index f1f5bf2ad2..c7a509b80c 100644
--- a/Library/Homebrew/cli/named_args.rb
+++ b/Library/Homebrew/cli/named_args.rb
@@ -99,8 +99,6 @@ module Homebrew
           begin
             return Cask::CaskLoader.load(name, config: Cask::Config.from_args(@parent))
           rescue Cask::CaskUnavailableError => e
-            retry if Tap.install_default_cask_tap_if_necessary
-
             raise e if only == :cask
           end
         end
diff --git a/Library/Homebrew/cmd/install.rb b/Library/Homebrew/cmd/install.rb
index 8be132b70a..14455e8bd1 100644
--- a/Library/Homebrew/cmd/install.rb
+++ b/Library/Homebrew/cmd/install.rb
@@ -153,8 +153,14 @@ module Homebrew
       EOS
     end
 
-    formulae, casks = args.named.to_formulae_and_casks
-                          .partition { |formula_or_cask| formula_or_cask.is_a?(Formula) }
+    begin
+      formulae, casks = args.named.to_formulae_and_casks
+                            .partition { |formula_or_cask| formula_or_cask.is_a?(Formula) }
+    rescue FormulaOrCaskUnavailableError, Cask::CaskUnavailableError => e
+      retry if Tap.install_default_cask_tap_if_necessary(force: args.cask?)
+
+      raise e
+    end
 
     if casks.any?
       Cask::Cmd::Install.install_casks(
diff --git a/Library/Homebrew/cmd/untap.rb b/Library/Homebrew/cmd/untap.rb
index e00d6ae9e7..33f56c4ba8 100644
--- a/Library/Homebrew/cmd/untap.rb
+++ b/Library/Homebrew/cmd/untap.rb
@@ -43,7 +43,7 @@ module Homebrew
         end
       end
 
-      tap.uninstall
+      tap.uninstall manual: true
     end
   end
 end
diff --git a/Library/Homebrew/extend/os/mac/tap.rb b/Library/Homebrew/extend/os/mac/tap.rb
index 495901ea68..ca2701238a 100644
--- a/Library/Homebrew/extend/os/mac/tap.rb
+++ b/Library/Homebrew/extend/os/mac/tap.rb
@@ -2,9 +2,11 @@
 # frozen_string_literal: true
 
 class Tap
-  def self.install_default_cask_tap_if_necessary
+  def self.install_default_cask_tap_if_necessary(force: false)
     return false if default_cask_tap.installed?
 
+    return false if !force && Tap.untapped_official_taps.include?(default_cask_tap.name)
+
     default_cask_tap.install
     true
   end
diff --git a/Library/Homebrew/tap.rb b/Library/Homebrew/tap.rb
index 2e75f812fa..da6a653fa1 100644
--- a/Library/Homebrew/tap.rb
+++ b/Library/Homebrew/tap.rb
@@ -67,8 +67,8 @@ class Tap
     @default_cask_tap ||= fetch("Homebrew", "cask")
   end
 
-  sig { returns(T::Boolean) }
-  def self.install_default_cask_tap_if_necessary
+  sig { params(force: T::Boolean).returns(T::Boolean) }
+  def self.install_default_cask_tap_if_necessary(force: false)
     false
   end
 
@@ -326,6 +326,17 @@ class Tap
                            .update_from_formula_names!(formula_names)
     end
 
+    if official?
+      untapped = self.class.untapped_official_taps
+      untapped -= [name]
+
+      if untapped.empty?
+        Homebrew::Settings.delete :untapped
+      else
+        Homebrew::Settings.write :untapped, untapped.join(";")
+      end
+    end
+
     return if clone_target
     return unless private?
     return if quiet
@@ -352,7 +363,7 @@ class Tap
   end
 
   # Uninstall this {Tap}.
-  def uninstall
+  def uninstall(manual: false)
     require "descriptions"
     raise TapUnavailableError, name unless installed?
 
@@ -374,6 +385,14 @@ class Tap
 
     Commands.rebuild_commands_completion_list
     clear_cache
+
+    return if !manual || !official?
+
+    untapped = self.class.untapped_official_taps
+    return if untapped.include? name
+
+    untapped << name
+    Homebrew::Settings.write :untapped, untapped.join(";")
   end
 
   # True if the {#remote} of {Tap} is customized.
@@ -624,6 +643,12 @@ class Tap
     Pathname.glob TAP_DIRECTORY/"*/*/cmd"
   end
 
+  # An array of official taps that have been manually untapped
+  sig { returns(T::Array[String]) }
+  def self.untapped_official_taps
+    Homebrew::Settings.read(:untapped)&.split(";") || []
+  end
+
   # @private
   def formula_file_to_name(file)
     "#{name}/#{file.basename(".rb")}"