Everyone has a different approach. I can hardly remember a thing that Tomas said in the many private lessons I had with him, but I remember his examples very well. One day I came to class with the John Duarte arrangement of the First Cello Suite by Bach. In this version, probably the most widely performed, the original in G major is transposed up a fifth to D major. Then the sixth string of the guitar is tuned down to D and bass lines are added. After I played, just the prelude, I think, Tomas picked up his eight-string guitar, dug around amongst his scores, and sight read the prelude from the original cello music in G major. It sounded so rich in comparison with the tinny sounding version up a fifth that I immediately gave up the idea of learning the Duarte arrangement. In the original key, it certainly did not need an added bass line. I was playing a six-string, not an eight-string guitar so Tomas suggested I try it in A major instead, which, years later, I did. After transposing and learning the whole suite I decided that it needed the third string to be in F# as well as the sixth in D, so I re-learned it. I also recorded the whole suite. Here is the prelude.
With Oscar Ghiglia, on the other hand, I hardly recall him playing anything in particular, but I remember what he said, very well. He loved to teach with metaphor. I remember him comparing the slow part of the prelude to the first lute suite by Bach to an opera plot. When the harmony got to a very dramatic V4/2 chord, he uttered in a deep voice: "revenge!" It seemed to perfectly capture the drama of the moment. Another time he might teach the same passage with an entirely different metaphor. I remember the devastating critique he gave of one woman's Bach: "you played that like you were going shopping!"
But I think all teachers give little demonstrations of how a phrase might go best, or how to balance a certain harmony.
Pepe Romero seemed to take a two-pronged approach: on the one hand he really focussed on technique. Uniquely among all the master classes I have seen, he would start each session with ten or fifteen minutes of technique with everyone playing together. He has some great exercises and I use them to this day to warm up and maintain my technique. One happy result of this was that nearly every guitarist had, by the end of the course, a much higher level of technical confidence. The importance of this cannot be over-rated. The other part of his approach was perhaps psychological. He talked about things like not playing from ego and about having a spiritual base. When it came to the music, he didn't say a lot. I think he has a very instinctive approach.
Oh, one other thing about José Tomas' approach: he had a scholarly side and also was an absolute master of fingerings. His editions of Bach or Scarlatti or Weiss were always the most practically and efficiently fingered.
Frankly, I don't remember a darn thing Leo Brouwer said either of the times I played for him--oh, apart from him asking about my odd sitting position the first time. I used to sit with the guitar positively wedged into my left thigh and tilting very forward.
One very funny thing I remember from Abel Carlevaro's master classes: he would say the same thing to every player: "you have two problems, the right hand and the left hand." True enough!
One more thing about Oscar Ghiglia: he had a sardonic side and seemed to really dislike everything about Argentina. I made the mistake of playing a piece by Máximo Diego Pujol, a guitarist-composer from Buenos Aires, for him once and all he did was tell a really disgusting joke about Argentinians. This was the piece.
One final thought about teaching: hardly any style or method gets to the really nitty-gritty core of what you need to play music. I think it boils down to concentration: if you have really good focus and concentration, then you can use your musicality and technical command at its best. If not, then the performance will come apart. So however you work, you need to develop your focus and concentration. I don't recall any teachers talking much about that...
Let's end with a fine performance by a young Canadian guitarist who seems to have this concentration thing down. This is Drew Henderson playing the Allegro from the Violin Sonata No. 2 BWV 1003 by J. S. Bach.