No need to apologise.And these functions rely on the ETS load and there would be no light and heat if ETS turned off, even if loco was idling?
Sorry to be dense.
To clarify - ETS is Electric Train Supply which powers the hotel load as you correctly call it, which is all the things that make a train carriage a nice place to be (light, heat, sockets for phones, water heaters, ovens and coffee machines in the buffet, etc).
It can be supplied by a generator connected to the locomotive engine or by a separate engine - either in the locomotive itself or in Chiltern's case by a diesel generator in the DVT. With DMUs the generator is normally connected to the drive engines in each powered carriage. The energy for the ETS generator has to come from somewhere so switching it to 'ON' in the locomotive means the engine has to run faster.
With regards to lighting, coaches have a battery which can supply the lighting circuit when there is no ETS supply available, but they have a limited capacity (I would think 30 minutes to a couple hour's lighting at most) and cannot power heavy loads such as the HVAC system or water heaters or ovens.
So, if the loco is idling with the ETS switched off the idle speed would be lower but the lights would be running off battery and there would be no heating or ventilation, nor could the cleaners plug a vacuum cleaner in or have any hot water.
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