Automation time trigger not firing

Configuration
3

If you want to use a Template Sensor as the source for a Time Trigger, its device_class must be timestamp and its state value should be a datetime object or a timestamp in ISO 8601 format.

sensor: 
  - platform: template
    sensors:
      next_fire:
        friendly_name: "Today’s time to fire"
        device_class: timestamp
        value_template: >
          {% if is_state('binary_sensor.holiday_sensor', 'on') %}
            {% set entity = 'input_datetime.fire_time_holiday' %}
          {% elif now().weekday() in [5, 6] %}
            {% set entity = 'input_datetime.fire_time_weekend' %}
          {% else %}
            {% set entity = 'input_datetime.fire_time_weekdays' %}
          {% endif %}
          {{ today_at(states(entity)).isoformat() }}

The following version of the template reduces some of the redundancy present in the previous version.

sensor: 
  - platform: template
    sensors:
      next_fire:
        friendly_name: "Today’s time to fire"
        device_class: timestamp
        value_template: >
          {% if is_state('binary_sensor.holiday_sensor', 'on') %}
            {% set entity = 'holiday' %}
          {% elif now().weekday() in [5, 6] %}
            {% set entity = 'weekend' %}
          {% else %}
            {% set entity = 'weekdays' %}
          {% endif %}
          {{ today_at(states('input_datetime.fire_time_' ~ entity)).isoformat() }}

EDIT

If this Template Sensor will be used by just one automation then you may as well just create a Template Trigger and eliminate the Template Sensor.

alias: example
trigger:
  - platform: template
    value_template: >
      {% set entity = 'holiday' if is_state('binary_sensor.holiday_sensor', 'on') 
         else 'weekend' if now().weekday() in [5, 6]
         else 'weekdays' %}
      {{ now().strftime('%H:%M:00') == states('input_datetime.fire_time_' ~ entity) }}
condition: []
action:
  ... your actions ...