We have lighting!
The case lights have been installed, consisting of two 1-meter LED light strips. These particular ones (3866 from Adafruit) are encased in a silicone casing that serves as a diffuser and avoids the visible hot-spot problem typical of LED strips. I was a bit concerned with bonding the silicone, but E6000 worked well and has a temporary, if potent, stench. I elected to only light the front two posts instead of the four originally considered, to add focus. to the dial section of the clock.