EE encompasses a lot of "engineering that takes hard math" at a professional and research level (similar to "hard CS," just different fields of math), so it is very hard to do as an undergrad, when your background in complex analysis and E&M is weak. Early classes on circuits in EE will usually take shortcuts using known circuit structures and simplified models. The abstraction underneath the field of analog circuits…
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.
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.