From what I've seen in my limited time, is fault finding needs a certain logical quality that folks either have or do not have, if you have it then with an understanding of the workings of the failed system and training in fault finding procedures you can do it, without that basic 'knack' for it, all the training in the work is usless.
You sometimes see chaps on site installing stuff by rote without understanding (or wanting to) why it works, a domestic spark will be connecting a heating system for instance and they will have a dog eared drawing by the side of them showing what colour on the 3 port valve goes to what, they will connect it correctly as per drawing and if all the parts are good, it'll work, but if it doesn't work they will not know where to start.
I suppose the missing thing is, is the internal need to understand why it works, rather than just accepting that you connect it like this, and it works.
So moving on, if you are alright at fault finding in one sector/environment, then you have a good starting point, you need to learn how the stuff in your new environment works, any specific fault finding procedures to it, possible pitfalls with it, and the common points of failure etc, but if you have the basic ability to fault find then learning how new bits of equipment work is something that can be done