I have never had any formal training in photography, which to some degree I regret. I've had a lot of formal training in lots of other things, though, including quite a few piano lessons.
Something I have harped on in the past, and no doubt will harp on in future, is this idea of vocabulary. The idea is simply to have in your mind a large number of bits and pieces of the raw material of photographs. These are lighting idioms, compositional idioms, post-processing effects, tricks for getting the subject to smile, anything, and everything. You gain this vocabulary by looking at pictures, for the most part, but also by reading (or consuming other media) about photography and about how pictures are made, and by doing photography.
You wouldn't try to write a poem without knowing a lot of words. Even Dr. Geisel knew a lot of words, even though he used as few as 50 to write a book. Knowing a lot of words makes you comfortable with the ones you're using. It gives you a larger pool of words to pick from, even if you're only going to wind up using a few. If you don't know a lot of words, then you cannot pick the right word, for starters, and (this is the important part) you're going to have fewer ideas about what to say.
When you learn to play the piano in a formal setting, you learn a lot of notation. You learn a notation for playing notes in a so-called staccato fashion, where each note is struck very briefly and released immediately, making a short percussive TINK sound. Contrariwise, you learn notation which means to connect a series of notes together in a phrase, and to leave a perceptible space after before beginning the next phrase. More importantly, you learn that there is the possibility of degrees and of connectedness between notes. You learn to phrase staccato notes together. You can separate legato phrases. You learn that there are degrees of length of a note. While it may be notated as a quarter note, indicating that it should be played for such and such a time (relative to the pacing of the piece) but that you can shorten that a little or a lot, and that this will result in different results.
Working with a teacher, you spend a lot of time working out how you want to use these bits of vocabulary. How can I use these ideas of phrasing, and of playing this note slightly louder than that note, and a thousand other things, to express what I want to express. Glenn Gould, it may be assumed, had at his command the entire vocabulary of the piano. For a specific piece he might well have selected a fairly small subset, he was famous for his pointillist readings of Bach, heavy with a staccato touch. Surely, though, his ability to render a piece in this manner was supported by his complete command of legato, and everything else. His ability to play the same piece extremely fluidly surely allowed him to manage the pointillism better, to select the exact degree of pointillism he wanted.
More to the point, though, his understanding of the wider vocabulary gave him the raw material to choose from, to select pointillism where he felt it right, and to select a more fluid style where that better served the music. Without the ability to imagine and experiment with a wide array of sounds, how could he have best selected the sound that served his needs?
I submit that, without the deep vocabulary, Gould might never have found his pointillist interpretation.
This is, sadly, unknowable. There's simply no way anyone gets to be much good at playing the piano without a decent teacher, and a decent teacher will generally make sure that you have a deep vocabulary on hand. Vocabulary building is absolutely central to teaching music, and many other fine arts. There is not, as far as I am aware, any similar process in the teaching of photography, but fairly obviously there should be.
As I read and learn and think about the problems of inspiration, and of making pictures that you actually like, and so on, the more it becomes clear to me that vocabulary is terribly, terribly important in photography. You've got to know a lot of little things, to give you a rich pool of ideas and raw material. It is from this pool of ideas that your ideas will come. They may come in a single Eureka! moment, they might be teased out by a process of refinement, but without the large vocabulary you're not likely to have much success.
How do you get the vocabulary? The same way you get the one made of words. Mainly, you "read", secondarily, you "write". Look at a lot of pictures. Look up the "words" you don't know, by which I mean figure out how the thing was done. Go take pictures, too, try things out. Try out things you don't think will please you. You don't think you'll ever use flash? Go take some anyways, that work will inform your landscapes, I promise. Shoot black and white, shoot color. Shoot portraits and street. Copy things you've seen. Fool around in your photo editor, trying to re-create effects you've seen, whether you like them or not. Read up on effects, how they were done in the darkroom and how they are done today.
There are degrees of knowledge here. You can recognize a visual effect when you see it, as you might recognize staccato. You might have some passing familiarity with how to produce an effect, or an idiom. You might feel extremely comfortable with some element of the photographic vocabulary. There is some value in each. Even a passing awareness of a photographic idea might inform an inspired moment, you might say "Oh man, THAT look, THAT would be PERFECT!" without having the foggiest notion of how to produce that look. I theorize, though, that your unconscious processes are more likely to seize upon just the right thing the more thoroughly you understand it. The inspiration machine that searches for solutions while you shower is, it seems reasonable, more likely to seize upon solutions you can execute than upon solutions you cannot.
A long, long time ago I wrote about the Second Worst Advice which is to just go out and shoot. That makes about as much sense as sitting down at the piano and poking notes at random. Go out and shoot, by all means, but with a plan. Today, I will work on phrasing. Today, I will work on black and white pictures of people. Today I will write a sonnet, however awful. Today I will take a still life backlit with flash. Today I will expand my vocabulary thus.
Vocabulary is the fuel of inspiration.