Si, I think, is easy. Think of Si as really, really, REALLY strongly felt hunches or gut feelings about things (as dom or aux). It's a huge capacity to remember things with a level of detail you and I cannot imagine. It's loyalty, integrity, and a very solid inner moral compass. Si is being so in tune with how your body feels that you know something's wrong long before any symptoms start showing overtly. Si is also stubborness, closed mindedness, bigoted attitudes, jumping to conclusions, and generally acting like a bull in a china shop ALL THE TIME. Si is having nothing but a hammer and treating the whole world like a nail, and still thinking you're right for doing it.
This description is misleading and almost entirely incorrect.
Si is not really physical. I would never say that Si means being in tune with your body. Si is only "physical" in the sense that it is based on sensory memory, and not on intuition and connecting dots (the dot-connecting is Ne). Sometimes it is like a gut feeling, but it's a gut feeling based on prior experience -- you may not remember that experience right away, but that precedent is constantly being referenced. The experience could have happened to someone else, in which case the experience is only sensory because you heard (with your ears) or read (with your eyes) someone discussing it.
Si is like being chained to an encyclopedia, or a filing cabinet full of documents. Before you can act on anything, or come to any conclusions, you have to reference those documents. All of your internal definitions are based on those documents. If one of them is rendered invalid, you have to put a replacement document into the same slot. Every single event that has ever happened to you, that you've ever read about, that ever registered with you in passing, is present in those documents -- and you may not even realize that you're referencing them, when you're referencing them. Only sometimes will an Si-user consciously think "What did others do in this situation, that I can learn from?" The rest of the time, it may, as you said, be a "gut feeling" -- thinking "that's unusual", because you've never seen anything done like that before, but not consciously going through every contrasting experience before thinking that.
The hammer is Te or Fe, not Si. Si is not about action. Si is about collecting and referencing data. Your "bull in a china shop" metaphor is much more about extroverted functions being backed by Si, than it is about Si itself.
Here's my favorite explanation of Si (in contrast with Ni):
[quote="The Introverted Sensation Function (Si) and Misconceptions", from Personality Cafe]The Introverted Sensation function can be explained more clearly with a scenario, such as making a particular sandwich. This sandwich is composed of mustard, mayo, lettuce, tomato, swiss, and ham.
Let’s say we have an Si user who is standing in the kitchen with the recipe and ingredients for this sandwich at a table. This will be the first time the Si user will ever make a sandwich or even seen a sandwich and thus his mind’s slate is clean. The Si user will read through the recipe and attempt to follow the instructions one by one to construct this sandwhich.
First, it tells him to use mustard and mayo on one side of each bread slices. Then it tells him to place lettuce, tomato, swiss, and finally ham in that exact order on top of one slice of bread with the condiment side facing upward. Lastly, it tells him to top it off with the second bread slice with the condiment side facing downward. He finishes.
Now he is to make a second sandwich without the help of the recipe. The Si user’s memory ispoor, unfortunately, so he can’t remember the recipe from heart, HOWEVER, he can “feel†out the sensation as he makes it. The Si user will have a sensation that tells him, wasn’t it the bread slice first that needs to be covered with mustard and mayo? He does not need to even say this. His gut feeling will tell him that probably is the first correct approach. His gut feeling will also tell him it was probably lettuce and tomato next in that order. Now he is almost finished but he is stuck. He can’t remember the next step. He tries to put ham on, but wait!
A sudden shock in his system.
“This doesn’t feel right,†the Si user says. He decides to try another item and places the swiss on top instead. Suddenly, his body tells him “This feels right,†and finally proceeds to place the ham on the sandwich. So far, it all feels “correctâ€. The Si user then continues to finish the sandwich with the final bread slice.
So the Si-user I used in this example has terrible memory. He cannot remember the recipe step by step, what items go in what order, how to start, or how to finish, at least in a differentiated manner. His body, however, remembers the sensation because he did it before. The first time he makes a sandwich was his development of an internalized sensation blueprint and so the next time he makes a sandwich, he has this internal sensation to utilize as a guide.
Introverted Intuition (Ni) Comparison/Contrast
Ni users, however, do not operate in this manner. Each time an Ni-user makes a sandwich, it isALWAYS a clean slate, at least until the information is finally well processed into the Psyche’s memory. As an Ni-user, I’ve often been told, “Oh come on, you did this 100 times, can’t you remember?†and I would respond, “I’m sorry, I can’t!†I can’t feel out the steps based on previous experiences. What an Ni user can do, however, is rely on “possibility hunches†to get things done. Ni does this by intuiting based on previously learned "principles and patterns" rather than the sensational experiences that Si learns.
An Ni user does not need to use Si to get the same job done. Both functions operate in different ways, but regardless, are capable of achieving the exact same result and thus, the similarity of results between Ni and Si sprouts the confusion among many.
So for an Ni user, every time he make a sandwich, he has to rely on intuition to get the sandwich constructed, despite the lack of prior experience. He can “feel†that the bread could “possiblyâ€have mustard and mayo on first. The Ni can visualize this and see just what the end result of the sandwich could be if he places mayo and mustard on each slice of bread. If his gut feeling believes it is correct, he will do this. His gut feeling will also visualize what item should go next. The ham? Swiss? Lettuce? Tomato? Often times, the Ni function will change its gut feeling each time the Ni-user makes a new sandwich. Because of this method, however, each time the Ni user makes a sandwich it can be different, whereas the Si user is more capable of repeating the same exact steps over and over.[/quote]