I think of Neurocentric training as any task that either requires extreme, acutely focused attention or task that is done with extreme, acutely focused attention.
So a great example of an inherently neurocentric training tool is slacklining, whereby one is required to pay exquisite attention to the "feel" of what is happening in order to constantly maintain balance. Now of course this quality dissolves as one improves in slacklining so in order to continue to raise the level of 'neurocentricity' as one develops skill perhaps the height is elevated, the distance between posts is lengthened, it is done blind-folded, etc. Other examples are rock climbing, single-trak biking, the internal martial arts in a combat situation, any combat situation for that matter.
An example of a task often used in conditioning made more neurocentric is running while paying incredibly close attention to the precise location of first contact on footfall. Is it the heel or ball of the foot? Medial or lateral aspect? How does the left compare to the right? How does a subsequent step feel in relation to the previous step? Or running can be made into a task that requires dedicated focus by running on a narrow surface such as a curb in which a mis step could lead to injury.
This can be applied to literally any form of training, conditioning or activity and I would argue that along with great coaching and natural talent it is the intense focus expressed as the interest in these details that makes the Jordans, Lideckys, and Messis of the world.
How you might make a kettle bell swing more neurocentric, for example, might be to note an object in the background and make note of when the kettle bell reaches its apex in front of you where it is in relation to that object, and not necessarily try to line it up every time, but simply notice.
Breath timing is another great way to make any aspect of training more neurocentric. Going back to the running example, you can note the steps-to-breath ratio or take slightly fuller breaths and notice how it changes the mechanics of your stride, do you take longer strides on a full breath or after you've exhaled?
Erwann Lecorre is great at setting up challenges that require steadfast focus because they consist of primarily balance, coordination, proprioception challenges on discontinuous surfaces that lead to falls if not properly engaged. Andreo Spina's FRC/Kinstretch system requires the participant to engage this high level of attention -without this level of intent and attention you're not doing Kinstretch - creating full irradition, complete articular movements and PAILs and RAILs all require complete focus and attention.
Using an example cited in an earlier article, Post Standing from various schools of the internal martial arts is not an endurance exercise as it might appear, but an exercise in noting joint positions, muscular tone, relationships between the aspects of the body, breath quality all with as little muscular effort as possible. In the absence of a sharply focused mind it is an endurance exercise for postural muscles. In the presence of a sharply focused mind it is a training of neuromuscular control that improves the quality of the sensory-motor system by drawing more finely detailed maps of our somatosensory cortex which leads to a host of documented improvements in health and movement.