What about a photodiode (I think thats the name) - something that is high impedance when it's dark and conducts when its light, connected to a battery powered a

What about a photodiode (I think thats the name) - something that is high impedance when it's dark and conducts when its light, connected to a battery powered analog watch that you set to midnight? It would give you total time open, and you could either reset it or just write down the time whenever you opened the box yourself.