The image above is from the first walk sequence. This demonstrates that the object was by her left side early on in the filming.
The image above is a bit harder to see but I believe that the object is visible at the lower extremity of the arm on the left side.
Perhaps this might explain why she would have a chunk of hair in her left hand in frame 352 above.
I will be carefully scrutinizing the film to see how many times this object can be seen.
Another great piece of visual detective work. For what it’s worth, to me, it looks like a stick.