The only two conditions where the dead body won't do anything is:
-If you have already collected the effect
-If you have used the Wing effect prior to interacting with it.
If the dead body is swinging from sides to sides, it means you're able to get the effect from it. If you're not able to get it in these conditions, it either means you aren't interacting with it properly (somehow) or a glitch makes it impossible for you to interact with stuff at all (which wouldn't be that surprising, given my track record).