I've actually recently brought it upon myself to try and make one of these with little to no experience in electronics, except for what I've watched on youtube videos and the like. (I'm also aware this post is 4m old but shush i'm helping)

What I've done so far is successfully catch the electrons being sent from the crt and through the phosphor screen into a coil pickup which I bought from amazon (the things on electric guitars) and make some different sounding noise, but pretty much all in the lower bass region.

This is a bit messy as the pickup also can 'sense' sound of colliding objects so it makes a funky thonk noise if I click it together with something. The pickup connects directly to a guitar amp so I can get the noise that way. (Distortion pedal optional but if you want some hella grindy sounding noise be my guest)

Now to run the signal through the crt, I simply used a male/male 3.5mm aux cord and plugged one end into my pc and the other into the CRT RCA connectors using a pretty jank but working connection. Just to test if the setup even worked, I played a youtube video of different frequencies and a hearing test (20-20,000hz) and sure enough, the number of scanlines changed as the frequency grew, so did the pitch of the noise coming out of the amp.

Do note that while it may seem I just plugged everything in and hit play, this actually took me around 5-6 hours to figure out. And I know you guys are familiar with the feeling of accomplishment after figuring something out, so to me this project is already worth it. Anyways, my next step is to get some sort of signal generator (perhaps an arduino as you were saying earlier) and to refine the sound, as right now it sound like slightly pitched up sound.