Both are correct, but 'kept' implies that this was exceptional, 'had' is more a bald statement of fact.

'Kept' means that the light stayed on all night. 'Had' could be for any length of time. It just suggests that at some point last night, your light was switched on. For example, I had the light on in my room so a mosquito flew in, I turned it off and the mosquito flew out again. If you wanted to mean that the light was on all night then you would need to add this information to the sentence. 'Last night I had the light on in my room all night'.

Thanks

Yes, I would say "kept" more naturally. Like the person below, using the word "kept" means that you did it on purpose.