Add precedent case for GH-84644

Author: johnslavik

Lib/test/test_functools.py

@@ -3274,6 +3274,22 @@ def _(arg, extra: int):
             "Use either `@register(some_class)` or add a type annotation "
             f"to parameter 'arg' of your callable.")
 
+        with self.assertRaises(TypeError) as exc:
+            # See GH-84644.
+
+            @functools.singledispatch
+            def func(arg):...
+
+            @func.register
+            def _int(arg) -> int:...
+
+        self.assertStartsWith(str(exc.exception), msg_prefix +
+            "<function TestSingleDispatch.test_invalid_registrations.<locals>._"
+        )
+        self.assertEndsWith(str(exc.exception),
+            "Use either `@register(some_class)` or add a type annotation "
+            f"to parameter 'arg' of your callable.")
+
         with self.assertRaises(TypeError) as exc:
             @i.register
             def _(arg: typing.Iterable[str]):