The only absolute is that there are no absolutes.
Every scenario discussed, gut shot, liver shot, grazed, large muscle hit, etc have no hard and fast reaction by the deer.
For instance I would say a gut shot deer usually reacts by tucking it's tail and hunching up. But I can also guarantee that such a scenario isn't 100 percent the case. I can say that because I gut shot a buck 2 years ago that ran off full tilt with flag waving. That's just 1 example. I'm sure others can describe similar experiences. How the deer reacts is just one piece of a sometimes complex puzzle.