My post on wind shadows sparked off a stream of comments from Tillerman. At first I thought he was trying to trick me into saying something incorrect, but it seems he was just trying to figure it out for himself.
Wind indicators point to windward, but they are affected by apparent wind, so a more accurate description would be that you are potentially in someone's wind shadow when you are on the imaginary line drawn straight downwind from the windward boat's sail plan.
Straight downwind. The wind shadow is not shifted by the movement of the boat in my mental model.
If you imagine a fast boat like a catamaran sailing on a broad reach (with respect to the true wind direction) but with the sails trimmed in to his apparent wind direction. The wind shadow of the catamaran must still extend downwind. If it extends along the apparent wind angle then it would extend upwind. There will be a region of turbulent air following the path of the boat, but this is turbulence, not a wind shadow.
Also, imagine a large powerboat moving quickly in a direction perpendicular to the true wind direction. It will still have a wind shadow extending downwind from its beam even though the apparent wind angle on the boat is the same as its direction of travel.