Intermediate Saturation Equilibrium
This is the tricky equilibrium and the one that will happen.
Let's divide the the final equilibrium into two possibilities. Over or under 50% saturation. If it's over 50%, we can simply use a the long rectangular sponge at the ceiling and make the perpetual waterfall. So, that leaves the last possible situation which is that the final equilibrium is somewhere between dry and 50% water saturation.
Will a sponge evaporate water in a 100% humidity environment?
Oh, it doesn't? Ok, so moisture content equilibrium is soaked. Remember, according to the 2nd law, things reach an equilibrium. So, you're saying that the perpetual waterfall is possible. You're saying that the 2nd law of thermo is wrong.
How can evaporation occur. the partial pressure of the H2O gas is less at the sponge than at the surface of the pool of the water. Another variable here is the shape of the meniscus of the water in the sponge poors. Concave on top, concave/convex on sides and convex on the bottom. But, we don't have to worry about the reason here. We know, that if the final equilibrium is soaked, then the 2nd law is wrong.
Ok, if the water in the sponge does evaporate then we can exploit this and create The Tilting Sponge Water Motor.