My Xperia Z tablet has a really bright LED that flashes when it is in standby (that is when the screen is blank). In fact, I am not sure it does it all the time, but it is very annoying if it is in the room at night. Is there any way to stop this from happening?
Perhaps the app Notification Light Widget will help you. It gives you a widget to manually enable/disable the light. Can't get a lot simpler than that!
Note that tweaking the notification LED is often a hit-or-miss operation with some devices. There's no promise that it'll work perfectly. Give it a shot and let us know how it goes!