Simulate object hanging on wire while keeping it manually animatable when needed?

I have a cloth simulated wire with vertices pined on the two sides of it to simulate the wire of a fishing rod.
The upper part of the wire is parented to the top of the fishing rod with an empty, and the cork & hook part is parented to the other side (bottom part of the wire).
Same situation as in the end of this tuto :

It work greatly to simulate the wire when i move the fishing rod, the only problem is I have to animate manually all the physical reactions of the cork / hook part. I basically parented it to the fishing rod so it follow it, but it don’t reproduce the physics movement a hanging cork to a wire would do normally.

Is there a way to can simulate physically the reaction of this cork when rod move, while keeping it attached to the wire, and while controlling the “influence” of the physics on it, so i can sometime take full control of it back for a precise movement animated manually (for exemple throwing it far, or keeping it static on a lake) ?

It’s quite complex situation here. Thanks to anyone that made the effort to read haha, don’t hesitate to share any idea.