In the past I have had students make a laser cut box for the base, but I am prototyping a carved version.
Here are the files, if it goes well I intend to make some awards for an upcoming film festival, then will see if the teacher who took over my old class wants to try it as a class project. Note: I haven't cut them yet, hope to try the first one this week. I'll probably use the laser for cutting and engraving the acrylic mainly to spread out the lines on machines, if you don't have a laser, it could be carved as well.
I am using a piece of kiln dried 2x3 (actual size 1.5" x 2.5") soft whitewood from Home Depot for the base (because it's dirt cheap). The components are a 9V battery, a simple toggle switch, one ea red, green and blue 5mm LED and a resistor, I don't have the BOM at hand for the exact value, but I can get it to you.
It's nice to have separate RGB lights because you can take the acrylic out of the base and play with color mixing in a dark room by shining it through your fingers - a little physics bonus!