If we put a floating ball at a high tide point on the ocean would it roll to low tide (assuming no friction)?

Question

Imagine we had a perfectly floating, frictionless ball we could place on the high tide point of the ocean, per the diagram below. Would it roll to low tide? If we originally placed it at low tide would it stay there? (I'm willing to give it a slight jiggle so it is not stuck at an unstable equilibrium)

According to this stack exchange answer, the answer appears to be yes, the ball will roll from high tide to low tide:

Water tends to find a level (ignoring tides)

Answer 1

The latter part of the sentence you quoted:

... a boat on the ocean will not drift towards the poles, because the oceans are essentially gravitationally flat

The ball would not roll towards low tide, because the tides are a gravitational effect, so everything on the surface of the ocean is already in gravitational equilibrium.

Of course this answer ignores waves, wind, currents, etc.