Following a wiggly path is 100% doable, it's just a pain in the neck. Here's what you have to do.
Start with a shape layer with a Rectangle first and then add a graph shape that extends beyond the rectangle. Then add Wiggle Paths to the graph shape and Merge Paths/Intersect to the pair so you end up with something like this:

I have shown you all modified properties on that layer.
Then pre-compose moving all attributes select the pre-comp and set up AutoTrace like this:

Here comes the pain in the neck. AutoTrace does not keep the first vertex in the same spot so you have to go through the timeline and set the first vertex to the same point for every frame. When that is done you can use the Create Nulls From Paths.JSX/Trace Path file to attach a null to the path, add the layer you want to follow the path and Shift + parent the layer to the null to snap it to the correct position and then just set the proper values for the first and last keyframe. You end up with this:

I don't know of any script that would AutoTrace a layer and keep the first vertex in the same spot and I don't even have any idea of how to begin to set that up, but if you have some time, and you set a keyboard shortcut for setting the first vertex you can eventually get it done. Here's the project file if you are interested.
Personally, I think it looks terrible. There's way too much going on for the eye to make any sense out of all the motion.