So is everything under control or still issues? Did it feel more like it was pulling the wheel away from you and center, or did it feel like it was trying to center over and over?
I can reinstall F1 2013, because I don’t remember in game settings nuances. But if you got the profiler installed and set right you should be good to go there so it would be in-game settings after that. In the meantime you can post screenshots of your in-game settings and I can see if something pops out.
Off the top of my head;
First Id try the simplest one; A lot of Codemasters games of that era have weird weird issues with vsync being on or off. It seems like it should be completely unrelated to a wheel but its worth trying. Try turning vsync ON.
Oscillation like that (if its pulling away from you) can be FFB strength related. Is your wheel super heavy/strong otherwise?
Centering spring could be set way too high.