diff --git a/django/utils/dateformat.py b/django/utils/dateformat.py
index 103bff7aae..f352c99f1a 100644
--- a/django/utils/dateformat.py
+++ b/django/utils/dateformat.py
@@ -56,20 +56,16 @@ class TimeFormat(Formatter):
         self.data = obj
         self.timezone = None
 
-        # We only support timezone when formatting datetime objects,
-        # not date objects (timezone information not appropriate),
-        # or time objects (against established django policy).
         if isinstance(obj, datetime):
+            # Timezone is only supported when formatting datetime objects, not
+            # date objects (timezone information not appropriate), or time
+            # objects (against established django policy).
             if is_naive(obj):
-                self.timezone = get_default_timezone()
+                timezone = get_default_timezone()
             else:
-                self.timezone = obj.tzinfo
-
-    @property
-    def _no_timezone_or_datetime_is_ambiguous_or_imaginary(self):
-        return not self.timezone or _datetime_ambiguous_or_imaginary(
-            self.data, self.timezone
-        )
+                timezone = obj.tzinfo
+            if not _datetime_ambiguous_or_imaginary(obj, timezone):
+                self.timezone = timezone
 
     def a(self):
         "'a.m.' or 'p.m.'"
@@ -136,7 +132,7 @@ class TimeFormat(Formatter):
 
         If timezone information is not available, return an empty string.
         """
-        if self._no_timezone_or_datetime_is_ambiguous_or_imaginary:
+        if self.timezone is None:
             return ""
 
         offset = self.timezone.utcoffset(self.data)
@@ -168,7 +164,7 @@ class TimeFormat(Formatter):
 
         If timezone information is not available, return an empty string.
         """
-        if self._no_timezone_or_datetime_is_ambiguous_or_imaginary:
+        if self.timezone is None:
             return ""
 
         return str(self.timezone.tzname(self.data))
@@ -185,7 +181,7 @@ class TimeFormat(Formatter):
 
         If timezone information is not available, return an empty string.
         """
-        if self._no_timezone_or_datetime_is_ambiguous_or_imaginary:
+        if self.timezone is None:
             return ""
 
         offset = self.timezone.utcoffset(self.data)
@@ -227,7 +223,7 @@ class DateFormat(TimeFormat):
 
     def I(self):  # NOQA: E743, E741
         "'1' if daylight saving time, '0' otherwise."
-        if self._no_timezone_or_datetime_is_ambiguous_or_imaginary:
+        if self.timezone is None:
             return ""
         return "1" if self.timezone.dst(self.data) else "0"