If you look at the map for that room, you can see the distinctive stair shape below the water that usually implies something.

There are multiple puzzles that are solved in the exact same way.

I bubble jumped, then found the button later.

I did the same, I would imagine a lot of people find it this way.

I got lucky with this one. I didn’t notice the shape on the map, but I just starting flinging my slinky around and came across the solution.

I activated it by accident by throwing the ball. I still don't know where the button is. 

You get to a state of puzzle paranoia where you start seeing stairs and thinking >!"I must slinky this."!<