I could be wrong but no I don't think the BBC Light didn't carry any service over night, They closed down at 2.00am while 5.30am they did in 1966 because I have an old Radio Times for July that year when the World Cup had just started.
The current practice of Radio 4 opting into the World Service at close down, and it being billed in the Radio Times, only started around 1995. Prior to that, Radio 4 would close down properly but the Droitwich LW transmitter only would then carry the World Service for a few hours (between 1 or 2am and 5am I think). This wasn't billed in the Radio Times as technically it wasn't Radio 4.
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The current practice of Radio 4 opting into the World Service at close down, and it being billed in the Radio Times, only started around 1995. Prior to that, Radio 4 would close down properly but the Droitwich LW transmitter only would then carry the World Service for a few hours (between 1 or 2am and 5am I think). This wasn't billed in the Radio Times as technically it wasn't Radio 4.