Backlit keyboard is OFF after recovering from clamshell mode
Unfortunately problems with Maverics and the build in camera is well known and document.

You have a little bit a odd one, but using the recommended procedure to try to fix it could not harm.

Resetting the PRAM and SMC is also recommended.

As for your flash light experiment:

As you shine the light in to the camera the keyboard back light is triggered indicating your camera is alive but not doing so well. The light sensitivity is not set properly.