How do I create a path from the player's movement?

I've wanted to try and experiment with making my characters long scarf dynamic, so that it flows and follows the player's movement. Conceptually, I was thinking perhaps somehow generating a path as the player moves, then have a sprite or a series of sprites follow that path.

If not, maybe something with physics?

I dunno, I'm not really sure where to begin with something like this, so I haven't actually built anything yet. I'm open to suggestion if anyone has done something like this before or has ideas.

The easiest way is to spawn a sprite with Fade out behavior at Player position on every tick.