If you have one nearby then I think you should have a look at Ikea.
They have a range of affordable low voltage LED lighting systems many of which have integrated sensors which turn on/off the light when a door is opened/closed
I understand they use an infrared sensor of some sort to detect the proximity of the door.
Links are for Ireland, but I'm sure you can find the same for your local store.
Here is the selection of lighting they offer
This one, may be of interest as it has integrated sensors,
This might be an earlier model, but there are lots of discussions and youtube videos online for reference.
Hope you find what you are looking for.