@Tom â€“ It's gonna sound really embarrassing that I didn't know about those pages.
Like you, I'm a DP-geek by trade, probably of similar age, who also writes music with a score.
I am also very interested in "figuring out how things work, so that I can then 'work' them." Stuff like "the harmonic series," how notes work for and against each other, "equal temperament," pure-geek stuff that, like working with computers themselves, is genuinely interesting and therefore enjoyable to me, as long as I can move it from the purely theoretical to something that's actually boots-on the-ground useful to me. (Okay, call me crazy that way ... (wink!) ... but I found my areas of genuine lifelong interest early.)
"How did he [know to] go in that direction? Because he knew that the hidden doorway was there â€“ and where it leads."
I also don't like obtuse explanations of what, I know, ought to be simple things. For example, I was offended that I had to memorize that line about little monkeys or risk failing the final exam â€“ which is another byzantine educational practice IMHO. No one ever told me what "modes" really were, nor how they worked, nor why. Same thing with the Circle of Fifths: better be able to draw it, or else, but for the most part that was the extent of where it went. (Maybe I just had a really bad teacher.)
Anyhow, maybe kids discover them when they put their hands on the keyboard in the "wrong" place, and maybe their music teachers reach over and grab their little hands and "correct" their "mistake." (As mine did.) But this also counts, to me, as a real musical discovery. You might do it entirely by accident. Or, you might compose a piece of music and sit down to play it â€“ or have MuseScore play it for you â€“ and "oops that's not the right starting point for this key" and maybe it sounds awful or maybe it sounds unexpectedly right. Different, but right. And yet, you don't know why. Much like the first time you paid attention to the black keys and ignored the white ones, and said dumb things to your kid brother that you thought sounded Chinese. If you were a geek like me, you said, "Why is that?" Maybe no one had the answer for you, but you wondered anyway.
Modes are something that you can easily do â€“ DAWs often have these features in their "piano rolls" â€“ and they are, or at least they were to me, a completely unexpected surprise. Once I realized what they actually were, and started seriously fooling around with them, it was another hidden door. Hid, for all this time, by a phrase about those dammed "little monkeys" and an 'educational' (sic) system that was content with rote memorization. Later on, I learned that some cool jazz stuff is done by putting the melody in one mode and the accompaniment in another. I had no idea; never thought of that. But I do understand why it could be done, and what its result might be, and yeah, I'm "nerding" around with that idea.