Ah, I see the problem now, I was thinking the main problem was the big flickering in brightness, I didn’t realize those were caustics. The white dots on the rocks are so small I missed them at first.
Well, the problem here is that you are reusing the rock’s very dark color texture as roughness. This makes the rocks very shiny, and the way you setup your color ramp makes them even more shiny (the rocks basically have a roughness of 0 over their whole surface and their speculars are very sharp and small).
This texture is not suitable to serve as roughness, because it has very little brightness variation. I would just disconnect it and set the rock’s roughness to a high value like you did. Rocks underwater usually don’t look shiny anyway, unless they are made of crystal.