I would try a simple approach to this first.
Create a tall photoshop document, use brushes to paint line(s) trying to keep the top and the bottom of the image as symmetric as possible the usen the offset plugin in AE to simulate a long continuous movement. You can also create different photoshop documents to keep it visually different.
Another approach can be doing the same thing in illustrator (because of its vectorial nature) then find a combination of plugins (roughen edges, some kind of distortion etc) in AE to make the lines more realistic…