Fault finding (much like that inspection element of Inspection and Testing) is something that can be taught fundamentaly but is honed and improved on over time; you have a basic start point (did any device trip, if so what device?, Is there continuity were there should be and inversely where there shouldn't be?, has the user done or changed anything recently? What has the weather been like...and so on) but improving on that and interpretating the answer comes over time.
I think your post is flawed and demonstrates a lack of knowledge regarding real fault finding, to confuse fault finding with inspection and testing blurs the lines between working with known standards and ensuring compliance on a go no go basis and fault finding where the test values achieved need to be interpreted correctly to have any idea of what you are looking for
It is difficult to teach fault finding beyond the basic principles, over time you develop your own methods how long it takes to do that can vary, when you have the production manager on your back because many £000's are being lost every hour it focuses you quite quickly, after a few years experience especially if you are involved in PPM work then you can often see developing faults before they become a fault
While fault finding has a number of basic principles it also combines a number of other wider skills not least choosing the optimum type of test equipment for the fault you are trying to locate and then understanding and interpreting the readings it gives you.
I agree that asking the right questions at the right technical level that the customer can process is another skill as sometimes you have to lead the customer through the problem to track / locate / narrow down the fault
Anyone can do testing, not everyone can do inspecting as 1 is 'simple' and thr other is complex.
I think you are wrong, there is more to testing than pressing a button on an MFT and expecting to see the right numbers, with inspecting it is simple when you can see what you are inspecting but good inspection is finding the things hidden in cupboards and joints buried in walls / hidden in trunking
Most of my fault finding skills come from working across all the industry sectors and a lot crosses over from sector to sector my apprenticeship was more industrial and commercial based where spending a little bit of time with the machine wiring diagram can save quite a bit of time locating the fault
Fault finding is like lock picking the more experience you have the easier and quicker the process becomes the key at times is not over thinking the problem and use the KISS principle although at times moving away from the day to day test equipment can save a lot of time