Unfortunately, with electronics repair and troubleshooting, when compared to repairing plumbing issues, the similarities end quickly. In a plumbing repair, the problems are usually obvious upon visual inspection and typically determined without specialized test equipment. Electronics repair is completely opposite of that. Occasionally, you may find a problem visually, like a burnt resistor, blown fuse, or a bulging capacitor, but the task afterward is to find the reason why a component failed. Some fail just due to age, and some have failure reasons that are just not discoverable without the training and equipment needed to follow a logical and experienced path.
Having just comparable DIY skills in electronics repair and troubleshooting would limit you to changing batteries, or replacing fuses. These things are fairly simple and would require only minimal skills and equipment, like the multimeter you said you now have. If that is simply the level you are after, you sound as if you would be there already, and it also sounds as if you are fine with that. That's good, too.
Quite the opposite is true. In my experience here, when you ask questions about a specific electronic component, or repair, there are usually many educated replies or directions to take afterward. After re-reading all of the comments in this thread, however, I do see where it appears you would rather have DIY Electronics Troubleshooting and Repair be as simple as installing plumbing parts. I would like that, too.

I can assure you, having done both of those things, there is just no comparison.
When I initiate an electronics repair, it is almost always for something I own. I don't do work for others, just because of the liability factor that comes with electricity and the possibilities of catastrophic failures if something would go wrong. I will take the chance for me, but not for anyone else. I have before, but it is rare and I make sure the risk is minimal.
For simple concepts, that "spiral method" works well. Electronics repair is often a multitude of combined "cores" attached together to complete one larger spiral. Simply using your spiral learning process doesn't work as well here. Too many "spirals," with too many "cores," if you will. There are many things that all of those cores combined together do that make the end product useful. Understanding each of those cores, and how they interact with each other, takes a lot of time and experience to understand, and even I know that, being a novice at what I do. Again, using your DIY Plumbing example, the plumbing challenge is straight forward and easy to follow. Not so with trying to troubleshoot a printed circuit board, especially if there are multiple layers to the board and a lot of components to check, as you mentioned in your initial posting, especially if you have no idea as to where to start.
My last comment would be for you not to sour on the experienced techs here based on their comments, but just know these guys will help if you come back with specific questions about a specific issue. Electronics repair is fun, when a repair is successful, and frustrating as all get out when it's not. A lot of time is seemingly wasted sometimes, but for me, I am always learning something new. Slowly, but at least something anyway.
Good luck, and take care.