Error Setting up Input_Boolean entity as programmable switch for HomeKit

I’m trying to select an input_boolean entity when configuring the final " Advanced Configuration" section of a HomeKit bridge.

The input_boolean is presented as selectable, but generates the error “Failed to set up”. Selecting any other item in the list works okay.

The logs presents the following;

Traceback (most recent call last):
  File "/usr/src/homeassistant/homeassistant/config_entries.py", line 444, in async_setup
    result = await component.async_setup_entry(hass, self)
             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/usr/src/homeassistant/homeassistant/components/homekit/__init__.py", line 357, in async_setup_entry
    await homekit.async_start()
  File "/usr/src/homeassistant/homeassistant/components/homekit/__init__.py", line 847, in async_start
    if not await self._async_create_accessories():
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/usr/src/homeassistant/homeassistant/components/homekit/__init__.py", line 1032, in _async_create_accessories
    acc = await self._async_create_bridge_accessory(entity_states)
          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/usr/src/homeassistant/homeassistant/components/homekit/__init__.py", line 978, in _async_create_bridge_accessory
    await self._async_add_trigger_accessories()
  File "/usr/src/homeassistant/homeassistant/components/homekit/__init__.py", line 998, in _async_add_trigger_accessories
    await device_automation.async_get_device_automations(
  File "/usr/src/homeassistant/homeassistant/components/device_automation/__init__.py", line 269, in async_get_device_automations
    for domain_results in await asyncio.gather(
                          ^^^^^^^^^^^^^^^^^^^^^
  File "/usr/src/homeassistant/homeassistant/components/device_automation/__init__.py", line 228, in _async_get_device_automations_from_domain
    return await asyncio.gather(  # type: ignore[no-any-return]
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/usr/src/homeassistant/homeassistant/components/mqtt/device_trigger.py", line 354, in async_get_triggers
    mqtt_data = get_mqtt_data(hass)
                ^^^^^^^^^^^^^^^^^^^
  File "/usr/src/homeassistant/homeassistant/components/mqtt/util.py", line 179, in get_mqtt_data
    mqtt_data = hass.data[DATA_MQTT]
                ~~~~~~~~~^^^^^^^^^^^
KeyError: 'mqtt'

Should I be able to add an input_boolean?