diff --git a/changes.d/6431.fix.md b/changes.d/6431.fix.md
new file mode 100644
index 0000000000..900bfee61d
--- /dev/null
+++ b/changes.d/6431.fix.md
@@ -0,0 +1 @@
+The `cycle point format` was imposing an undesirable constraint on `wall_clock` offsets, this has been fixed.
diff --git a/cylc/flow/task_proxy.py b/cylc/flow/task_proxy.py
index 4e7b60d6e0..0ba67438fc 100644
--- a/cylc/flow/task_proxy.py
+++ b/cylc/flow/task_proxy.py
@@ -48,7 +48,6 @@
 from cylc.flow.cycling.iso8601 import (
     point_parse,
     interval_parse,
-    ISO8601Interval
 )
 
 if TYPE_CHECKING:
@@ -424,14 +423,18 @@ def get_clock_trigger_time(
         """
         offset_str = offset_str if offset_str else 'P0Y'
         if offset_str not in self.clock_trigger_times:
+            # Convert ISO8601Point into metomi-isodatetime TimePoint at full
+            # second precision (N.B. it still dumps at the same precision
+            # as workflow cycle point format):
+            point_time = point_parse(str(point))
             if offset_str == 'P0Y':
-                trigger_time = point
+                trigger_time = point_time
             else:
-                trigger_time = point + ISO8601Interval(offset_str)
+                trigger_time = point_time + interval_parse(offset_str)
 
-            offset = int(
-                point_parse(str(trigger_time)).seconds_since_unix_epoch)
-            self.clock_trigger_times[offset_str] = offset
+            self.clock_trigger_times[offset_str] = int(
+                trigger_time.seconds_since_unix_epoch
+            )
         return self.clock_trigger_times[offset_str]
 
     def get_try_num(self):
diff --git a/tests/integration/test_xtrigger_mgr.py b/tests/integration/test_xtrigger_mgr.py
index d04c202bd4..73dd66fc2c 100644
--- a/tests/integration/test_xtrigger_mgr.py
+++ b/tests/integration/test_xtrigger_mgr.py
@@ -29,30 +29,38 @@ def get_task_ids(schd: Scheduler) -> Set[str]:
 
 
 async def test_2_xtriggers(flow, start, scheduler, monkeypatch):
-    """Test that if an itask has 2 wall_clock triggers with different
-    offsets that xtrigger manager gets both of them.
+    """Test that if an itask has 4 wall_clock triggers with different
+    offsets that xtrigger manager gets all of them.
 
     https://github.com/cylc/cylc-flow/issues/5783
 
     n.b. Clock 3 exists to check the memoization path is followed,
     and causing this test to give greater coverage.
+    Clock 4 & 5 test higher precision offsets than the CPF.
     """
     task_point = 1588636800                # 2020-05-05
     ten_years_ahead = 1904169600           # 2030-05-05
+    PT2H35M31S_ahead = 1588646131          # 2020-05-05 02:35:31
+    PT2H35M31S_behind = 1588627469         # 2020-05-04 21:24:29
     monkeypatch.setattr(
         'cylc.flow.xtriggers.wall_clock.time',
         lambda: ten_years_ahead - 1
     )
     id_ = flow({
+        'scheduler': {
+            'cycle point format': 'CCYY-MM-DD',
+        },
         'scheduling': {
             'initial cycle point': '2020-05-05',
             'xtriggers': {
                 'clock_1': 'wall_clock()',
                 'clock_2': 'wall_clock(offset=P10Y)',
                 'clock_3': 'wall_clock(offset=P10Y)',
+                'clock_4': 'wall_clock(offset=PT2H35M31S)',
+                'clock_5': 'wall_clock(offset=-PT2H35M31S)',
             },
             'graph': {
-                'R1': '@clock_1 & @clock_2 & @clock_3 => foo'
+                'R1': '@clock_1 & @clock_2 & @clock_3 & @clock_4 & @clock_5 => foo'
             }
         }
     })
@@ -62,16 +70,22 @@ async def test_2_xtriggers(flow, start, scheduler, monkeypatch):
         clock_1_ctx = schd.xtrigger_mgr.get_xtrig_ctx(foo_proxy, 'clock_1')
         clock_2_ctx = schd.xtrigger_mgr.get_xtrig_ctx(foo_proxy, 'clock_2')
         clock_3_ctx = schd.xtrigger_mgr.get_xtrig_ctx(foo_proxy, 'clock_2')
+        clock_4_ctx = schd.xtrigger_mgr.get_xtrig_ctx(foo_proxy, 'clock_4')
+        clock_5_ctx = schd.xtrigger_mgr.get_xtrig_ctx(foo_proxy, 'clock_5')
 
         assert clock_1_ctx.func_kwargs['trigger_time'] == task_point
         assert clock_2_ctx.func_kwargs['trigger_time'] == ten_years_ahead
         assert clock_3_ctx.func_kwargs['trigger_time'] == ten_years_ahead
+        assert clock_4_ctx.func_kwargs['trigger_time'] == PT2H35M31S_ahead
+        assert clock_5_ctx.func_kwargs['trigger_time'] == PT2H35M31S_behind
 
         schd.xtrigger_mgr.call_xtriggers_async(foo_proxy)
         assert foo_proxy.state.xtriggers == {
             'clock_1': True,
             'clock_2': False,
             'clock_3': False,
+            'clock_4': True,
+            'clock_5': True,
         }