The battery pack and switch for the lights are housed in the base of the chest. I ran them through the coil of the door stop into the clock panel. I left one light on the base side of the chest and used it to light up the on/off switch. The light switch consists of a small metal tube with a bead on the end which is lit up with one of the LEDs and glued onto the sliding switch of the battery pack.
To finish up:
Arrange the lights in the lid of the chest.
Place the control panel and attach with removable glue dots so that you can access the clock easily if needed.
Place the hands on the clock.
Turn on the lights.
A few final thought:
I have to say I am a bit disappointed by the amount of light produces, with the room lights off it is bright enough but during the day it is hard to read the time. I will have to find another brighter source for a back light.
Also I'm not to sure about the control panel, when I showed a friend he said it was not something you would want to take through airport security (that is not quite what I was going for). I had considered using a one litre ice cream container instead, perhaps next time. . .
I included a pdf of the clock panel if you want to make this yourself, though it is probably only useful if you use the same size container to hold it, alternately you can modify the image to adjust the size to your liking.