Happy new year!
To attempt to answer your question, the best way to learn a putting stroke is to first learn about what makes a good stroke, then learn how to make a good stroke, then learn how a good stroke feels, then learn how to make a good stroke that feels good, then learn how to feel whether you are making a good stroke, then learn how to make a good stroke without paying too much attention, then learn how to make a good stroke even if you're not paying attention, then learn how to make a good stroke when you are distracted, then forget how to make a good stroke and learn how to sink a putt.
Each of these is a separate stage in the process. Ultimately, you want a stroke pattern that you TARGET with in order to maximize the chances of sinking any given putt. This stroke pattern needs to be fairly simple for the golfer to feel and repeat, and ought to work with and enhance natural body movements and anatomy / biomechanics. The actual stroke pattern can vary for individuals, although there is probably a "best overall pattern" that would be best for a great majority of golfers (square setup, pendulum-like motion, etc.).
Learning what makes a good stroke is about the physics of putterface orientation, loft, launch conditions, and so forth, that makes a consistent straight roll with good touch or distance control -- square setup, ball ahead, square face at impact, good tempo, light and steady grip pressure, triangle intact, no wrist action, and so on. At this point, it is just teaching the student ABOUT the stroke, so the student understands the different aspects. Usually, this is a combination of lecturing and demonstrating, and allowing the student to try things out to see for himself. The student has to know wgat is important and why, so he can tell what is right and wrong, or what works and why it works that way.
Learning to make a stroke like the one thought best is, initially, monkey-see, monkey-do. You can teach it wuth rules, too, but start with "move this way" more than anything. Rules would include "no hands" because hands twist the putterface out of square; "elbows below shoulders" and "shoulders move in plane"; "lead elbow stays headed down the line parallel left"; "start the backstroke straight away from the ball"; "keep the pivoy steady"; and the like.
Once the student has this sorted out, he needs to focus on how it feels to make the movements he wants to happen. This is partly how it feels at setup, how it feels to start the motion, how it feels during the motion, and how it feels to finish off the motion. Thinking about starting the motion is a big part of this stage, and assessing the feelings at setup before starting the motion to make sure your positions are suitable for the motion you want to make is a big part, too. This is where your tip "Get Level" comes in. Mentally assessing positions and feelings so that the stroke feels right and good is the key here. Anything you can do to get the student to feel hands, wrists, shoulders, elbows, balance, etc., is probably good. How far are the hands from the thighs? What path in the air do the elbows follow? Where does the left shoulder go in space? How does the weight feel distributed in the feet? What about the hips? How does the head feel balanced? Are the eyes quiet? If you use drills or training aids, make sure the student knows what he is expected to FEEL from the exercise so he is tuned in to the right sort of feedback for the right reason, and knows why he is doing the exercise. For example, the purpose of a stroke track is not to watch the putterhead, but to sense how the body feels when the stroke is good.
Learning how to make a stroke that feels good is, again, mostly a process of paying attention to the body in adopting the setup, in preparing to start the stroke, in making the stroke, and in finishing the stroke. The difference bow is that you are more aware of body feelings as GOALS rather than thinking about "rules" or "positions." Tempo is a big focus here, and how tempo feels in different body parts at different points in the stroke. For example, how does the motion pattern of the downstroke match up with the motion pattern of the follow-through in terms of amplitude, speed, timing, etc. Does the stroke feel smooth and steady?
Learning to feel whether you are making a good stroke is a natural progression of the preceding stage. Once you focus on learning to make a stroke that feels good, and have focused on the feelings of a good stroke, you know what to expect. Knowing what to expect is the first step to making it happen that way. So you are constantly aware if the feelings are in or out of the expected pattern. This sort of monitoring is the real practice of the skill of the stroke. This is when the student gets going on his own towards mastery.
The other stages are about the mind-body relationship during putting. Feeling the food stroke is much more useful and consistent than thinking about technique and "trying" to do the technique correctly. The mind can be as empty as when you enjoy the feeling of the warm sun on the beach, or a nice breeze. Eventually, you want to save your focus for reading the putt, sensing distance and energy through the break, and visualizing the successful roll into the cup, so that actually executing the stroke is just as natural as breathing.
To respond to your very precise question, making repetitions alone probably won't change the stroke, but making repetitions with the intention of using this pattern for the stroke probably will. If you know what the stroke out to look and feel like, and how to make it jappen so it feels right, then repeating this intention and paying attention to these feelings will change the brain and make it more sensitive to this pattern of feelings and plans, so making this good stroke comes more naturally from the whole set of feelings and actions. When you setup, the good stroke starts to take shape just from the feelings in your feet!
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