diff --git a/Library/Homebrew/tap.rb b/Library/Homebrew/tap.rb
index 8e779c6ecf..2cf5efc378 100644
--- a/Library/Homebrew/tap.rb
+++ b/Library/Homebrew/tap.rb
@@ -402,6 +402,7 @@ class Tap
     end
 
     clear_cache
+    Tap.clear_cache
 
     $stderr.ohai "Tapping #{name}" unless quiet
     args =  %W[clone #{requested_remote} #{path}]
@@ -546,6 +547,7 @@ class Tap
 
     Commands.rebuild_commands_completion_list
     clear_cache
+    Tap.clear_cache
 
     return if !manual || !official?
 
@@ -931,27 +933,42 @@ class Tap
     other = Tap.fetch(other) if other.is_a?(String)
     other.is_a?(self.class) && name == other.name
   end
+  alias eql? ==
 
-  def self.each(&block)
-    return to_enum unless block
+  sig { returns(Integer) }
+  def hash
+    [self.class, name].hash
+  end
 
-    installed_taps = if TAP_DIRECTORY.directory?
-      TAP_DIRECTORY.subdirs
-                   .flat_map(&:subdirs)
-                   .map(&method(:from_path))
+  # All locally installed taps.
+  sig { returns(T::Array[Tap]) }
+  def self.installed
+    cache[:installed] ||= if TAP_DIRECTORY.directory?
+      TAP_DIRECTORY.subdirs.flat_map(&:subdirs).map(&method(:from_path))
     else
       []
     end
+  end
 
-    available_taps = if Homebrew::EnvConfig.no_install_from_api?
-      installed_taps
+  # All locally installed and core taps. Core taps might not be installed locally when using the API.
+  sig { returns(T::Array[Tap]) }
+  def self.all
+    cache[:all] ||= begin
+      core_taps = [
+        CoreTap.instance,
+        (CoreCaskTap.instance if OS.mac?), # rubocop:disable Homebrew/MoveToExtendOS
+      ].compact
+
+      installed | core_taps
+    end
+  end
+
+  def self.each(&block)
+    if Homebrew::EnvConfig.no_install_from_api?
+      installed.each(&block)
     else
-      default_taps = T.let([CoreTap.instance], T::Array[Tap])
-      default_taps << CoreCaskTap.instance if OS.mac? # rubocop:disable Homebrew/MoveToExtendOS
-      installed_taps + default_taps
-    end.sort_by(&:name).uniq
-
-    available_taps.each(&block)
+      all.each(&block)
+    end
   end
 
   # An array of all installed {Tap} names.
diff --git a/Library/Homebrew/test/spec_helper.rb b/Library/Homebrew/test/spec_helper.rb
index 48068f8f37..b8af2d24e9 100644
--- a/Library/Homebrew/test/spec_helper.rb
+++ b/Library/Homebrew/test/spec_helper.rb
@@ -204,7 +204,7 @@ RSpec.configure do |config|
   config.around do |example|
     Homebrew.raise_deprecation_exceptions = true
 
-    Tap.each(&:clear_cache)
+    Tap.installed.each(&:clear_cache)
     Cachable::Registry.clear_all_caches
     FormulaInstaller.clear_attempted
     FormulaInstaller.clear_installed
@@ -244,9 +244,6 @@ RSpec.configure do |config|
     rescue SystemExit => e
       example.example.set_exception(e)
     ensure
-      # This depends on `HOMEBREW_NO_INSTALL_FROM_API`.
-      Tap.each(&:clear_cache)
-
       ENV.replace(@__env)
       Context.current = Context::ContextStruct.new
 
@@ -257,6 +254,7 @@ RSpec.configure do |config|
       @__stderr.close
       @__stdin.close
 
+      Tap.all.each(&:clear_cache)
       Cachable::Registry.clear_all_caches
 
       FileUtils.rm_rf [