Interesting. My approach to hobbyist EE (actually embedded) is:
1. Learn soldering
2. Treat circuits like black boxes. If I need X amount of Y, e.g. I need a circuit to smooth the voltage, I pick one black box with adequate attributes.
However this is pretty introductory and I have no idea how to learn to fix old consoles. Sometimes it’s just a broken capacitor but I first need to figure out which part is broken.
Fixing old consoles is roughly...
a) inspect for obviously damaged components. Capacitors that leaked, chips that released the magic smoke, etc.
b) confirm voltages are good
c) inspect the inputs and outputs of the ics to see if they're doing what you expect
d) depending on the boards involved, a lot of checking if pin A is electrically connected to pin B when it should be. Sometimes traces get broken and need to be fixed up.
Circuits as black boxes is usually a very leaky abstraction, because how circuits work depends a lot on what’s connected to them. And they have plenty of attributes that can interact in very weird ways.
Fixing consoles is also treating circuits like black boxes :) . just gotta know what the black boxes are