Quit with the "shadowing" talk. As others have said, you have responsibilities. As a third year, you will retract, retract, retract, make the opening incision, cut, tie, snap, retract some more, operate one of the laparoscopic instruments (usually the camera), suction suction suction. At the end, the attending might step away and have you finish the suturing, or staple, then you apply the dressings, connect drains etc. Shadowing has nothing to do with it. The ED has nothing to do with it.
You dont have a class thrown in where you learn surgical stuff. You will have a daily lecture in one form or another (lecture, discussion, journal club, M&M, grand rounds, tumor board), where you will learn the pathophysiology of surgical disease - compartment syndrome, appendicitis, cholecystitis, diverticulitis... etc, or specific techniques like laparoscopy, or complications of a type of surgery. Basically, stuff that has nothing to do with the technical aspects of operating, but everything to do with surgery.
You learn surgical stuff by reading up on how the cases you'll be in are done. You'll watch and remember what you read. Things will start to make sense. You might be taught tiny little principles of operative technique - like pulling tissue straight up while cutting. You might be shouted at for doing something opposite of what the surgeon is doing by second nature.
On a surgical rotation you spend a lot of time managing the patient on the floor, before and after surgery. The OR time seems small in comparison.
Anyway. No shadowing, No nothing thrown in. No shadowing.