I'm not so sure methodical troubleshooting is something you can really teach. At least, I can't seem to. It's something I tend to be fairly good at, and when I try to help others they often seem to have not the slightest clue where to start. I can lay out a plan for them to follow, and they can follow it and get results, but then when the next problem comes along, once again they are lost.
Not necessarily electronics - despite an EE degree I have very little working experience as an EE, and none of that was really design work. But most any other system, be it computer networks, a model railway, small engines - I can usually figure out the problem fairly quickly.
Case in point of not knowing a reasonable way to go about it - I was having signal problems with my cable modem (and starting to get bad enough to cause issues with watching TV as well). After verifying a poor signal inside (though slightly annoyed they wouldn't take my word for it, I've had enough experience to know you can't), I think my next step would have been to check the signal at the house, just off the pole, rather than to go about the house and cut off all my nicely crimped connectors and put new ones on (sorry kid, I've been terminating coax longer than you've been alive). The work my way downstream to the point the signal degraded and then the problem would HAVE to be between there and the last point tested. Also not a very technical 'tech' - wasn't interested in seeing the signal levels my cable modem showed, just wanted me to do speed tests to prove it was a mere fraction of what I was supposed to get. So after all that proved fruitless, and I had all new ends on every cable in the house, NOW he goes outside, checks the line from the pole - OK, it's good there. So now he wants to run a new cable in the hardest possible place to fish a cable in my house, above the fire resistant ceiling of the garage - because just on the other side of the garage, it tested bad. There's only one problem - he tested the line from the pole BEFORE the lightning arrestor, and the line inside was of course AFTER it. I suggested he hook his fancy Fluke to the cable AFTER the arrestor and try that before digging out cable. Sure enough - bad. 5 minutes later, everything is back to normal. I don't get charged for this, so saving the guy an hour's worth of hard work didn't mean they made less money from me, in fact, I believe they are paid by how many calls they make in a day, so I helped the guy. But it seemed so obvious to me - I don't have mice or other critters in my house, so how could the cable up there, undisturbed, go bad, plus there were electrical storms shortly before the service went in the dumper. Had I even know that thing was there I probably would have just run off to the hardware store and replaced it myself - it took over a week of calling to finally get someone scheduled to come take a look in the first place.