Correct me if I'm wrong but if ANY door or the hatch is not closed properly, the blue display remains lit. If so, there's 1 item that remained on. If that's on, there may also be other electric consumers active as well. I don't know how the display is back lit, I thought it would be led or oled which shouldn't cause a flat battery in that time IMO.
rather than remove the lamp altogether, why not buy an equivalent brightness led bulb which will consume much less power.
If you know someone who can solder, you could also put a little audible device that is energised by the light circuit.