This looks like a fun project. I think it works so well, or at least, seams to in the video because LEDs are so damn efficient.
I would make it somewhat differently, but this is good. For one thing, I'd probably make it out of an LED flashlight, swapping out the batteries for a motor.
And then, when you have your flashlight ready, you can do this!
(Hat tip: David Cassatt)
The issue is getting the right gear motor, which is unspecified. :(
The gearing is going to be pretty bulky, unless you specifically design it to be not bulky. Usually these gear motors are designed for specific purpose mechanical devices where there is plenty of bulk to accommodate inefficient design.
Getting a high gear reduction requires multiple gears, unless a worm gear is used, but then the gear train can't be operated from the other end.