I'm not sure if I'm an Si user, but here is what makes sense to me as fitting the description:
good sense of my internal state
good muscle memory, able to "learn" things by watching others and feeling how it would be to do it
physical sense for energy, including a sense for how old objects and buildings are
unconsciously routinize things- it's hard to get into habits and hard to get out of them
little memory for facts unless they stand out somehow or are triggered by something
everything I see reminds me of things I associate with that kind of thing (Si-Ne?)
good navigation skills, both visual and kinesthetic
Edit: Another thing: I have a lot of what I feel like are past life memories, and I can sometimes sense other people's.
These things could be Se, and I'm an INFJ; either way I'm very curious.