diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 0ce32fcd822e0..ec36e53b97b3c 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -1554,6 +1554,9 @@ def ceil(self, freq, ambiguous="raise", nonexistent="raise"):
     # --------------------------------------------------------------
     # Frequency Methods
 
+    def _maybe_clear_freq(self):
+        self._freq = None
+
     def _with_freq(self, freq):
         """
         Helper to get a view on the same data, with a new freq.
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index a05dc717f83c1..b9a6df10d3630 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -474,9 +474,6 @@ def _check_compatible_with(self, other, setitem: bool = False):
             if not timezones.tz_compare(self.tz, other.tz):
                 raise ValueError(f"Timezones don't match. '{self.tz}' != '{other.tz}'")
 
-    def _maybe_clear_freq(self):
-        self._freq = None
-
     # -----------------------------------------------------------------
     # Descriptive Properties
 
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index d9ecbc874cd59..035e6e84c6ec8 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -313,9 +313,6 @@ def _check_compatible_with(self, other, setitem: bool = False):
         # we don't have anything to validate.
         pass
 
-    def _maybe_clear_freq(self):
-        self._freq = None
-
     # ----------------------------------------------------------------
     # Array-Like / EA-Interface Methods
 
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 40a6086f69f85..176fef13094fd 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -104,6 +104,16 @@ class DatetimeIndexOpsMixin(NDArrayBackedExtensionIndex):
     def _is_all_dates(self) -> bool:
         return True
 
+    def _shallow_copy(self, values=None, name: Label = lib.no_default):
+        name = self.name if name is lib.no_default else name
+
+        if values is not None:
+            return self._simple_new(values, name=name)
+
+        result = self._simple_new(self._data, name=name)
+        result._cache = self._cache
+        return result
+
     # ------------------------------------------------------------------------
     # Abstract data attributes
 
@@ -662,16 +672,6 @@ def _with_freq(self, freq):
         arr = self._data._with_freq(freq)
         return type(self)._simple_new(arr, name=self.name)
 
-    def _shallow_copy(self, values=None, name: Label = lib.no_default):
-        name = self.name if name is lib.no_default else name
-
-        if values is not None:
-            return self._simple_new(values, name=name)
-
-        result = self._simple_new(self._data, name=name)
-        result._cache = self._cache
-        return result
-
     # --------------------------------------------------------------------
     # Set Operation Methods
 
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index 44c20ad0de848..cff50bf0f1eab 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -4,7 +4,6 @@
 import numpy as np
 
 from pandas._libs import index as libindex
-from pandas._libs.lib import no_default
 from pandas._libs.tslibs import BaseOffset, Period, Resolution, Tick
 from pandas._libs.tslibs.parsing import DateParseError, parse_time_string
 from pandas._typing import DtypeObj, Label
@@ -278,16 +277,6 @@ def _has_complex_internals(self) -> bool:
         # used to avoid libreduction code paths, which raise or require conversion
         return True
 
-    def _shallow_copy(self, values=None, name: Label = no_default):
-        name = name if name is not no_default else self.name
-
-        if values is not None:
-            return self._simple_new(values, name=name)
-
-        result = self._simple_new(self._data, name=name)
-        result._cache = self._cache
-        return result
-
     def _maybe_convert_timedelta(self, other):
         """
         Convert timedelta-like input to an integer multiple of self.freq
@@ -341,7 +330,7 @@ def _mpl_repr(self):
 
     @property
     def _formatter_func(self):
-        return self.array._formatter(boxed=False)
+        return self._data._formatter(boxed=False)
 
     # ------------------------------------------------------------------------
     # Indexing
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index cf5fa4bbb3d75..84390822813cd 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -175,9 +175,7 @@ def _simple_new(cls, values: TimedeltaArray, name: Label = None):
 
     @property
     def _formatter_func(self):
-        from pandas.io.formats.format import get_format_timedelta64
-
-        return get_format_timedelta64(self, box=True)
+        return self._data._formatter()
 
     # -------------------------------------------------------------------