Maybe you can suggest something? Seems like you're the subject matter expert here. I mean you wouldn't make recommendations on something you know nothing about, right?
Looks a LOT like the endcap they put on the axle of a kids bike, trike, wagon, or any other wheeled riding toy. Most the time they are red or black. It would make a good crunching sound when ran over.
Is that the cap for your NOS bottle?
Kidding, that's not a part of your car.
If you were parked on a hill, that could account for the rough transfer from park to reverse.
"There are no finger prints under water."
I would also say not an item from your vehicle. Do you have any kids as neighbors? Likely something they just threw in your driveway.
Good luck with it and hope all is well.
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The ONLY thing I can come up with (car related anyway) is some kind of dust cover or similar thing for the shifter linkage where it meets the transmission... but probably not, especially being hard plastic. I don't know what your car looks like down there so I'm basically just making shit up. Whatever the case, stuff like that (small, threads are molded into the plastic, etc. Means its not designed to hold up to stress) generally aren't critical components. I wouldn't worry about it, car part or not.
Cfortune, anything that lives underneath a vehicle would not be that color after about 6 weeks on the road, let alone 13 years. As everyone else has stated, it is not likely from your car.
"There are no finger prints under water."