I do seem to remember a Y plan with supply to pump from boiler something like this.
I seem to remember it was to allow the boiler to cool before the pump turned off and of course it also has to hold open the motorised valve while it cools.
I will admit I had a lot of problems with my daughters Y plan as the diagram shows one micro switch but in fact there are around three micro switches inside the motorised valve so trying to test gets results which reading the diagram seem impossible.
In the end I replace the whole valve as I could not find a supplier for the micro switches on the Sunday I was doing the job. Lucky
Screwfix was open. She also at another time had problems with the PCB and my son replaced that for her.
To my understanding the thermostat does not control the boiler but it controls the motorised valve which once open then in turn works the boiler.
She has now moved house so I know no one with a Y plan any more. And am glad of that. However there is no connection to lights and no fault with a boiler should effect any lights.
What I have seen is people using three core cable to the cylinder thermostat and using the earth marked core for a non earth connection. This could result in a fault if the thermostat was changed from a double insulated to one requiring an earth and the miss marked cable was earthed.
The diagram shown is not mine can't remember where I got it from so can't really answer too many questions but it does show the pump connected separate to main boiler supply.