Why did Moses have to meet Pharaoh by the water at sunrise? The plain text only says that Pharaoh went out to the river (Exodus 7:15). Targum Pseudo-Jonathan on Exodus 7:15 tells us what Pharaoh was doing there: he cometh forth to observe divinations at the water as a magician.
The meturgeman unmasks the king. Pharaoh, divine in his own empire's theology, was actually a diviner — a man who read the Nile's surface for signs because he could not generate any himself. Every morning, before the business of the throne, Egypt's god went down to the water to ask the water what the day would bring.
This is why Moses is sent to meet him there. God is not intercepting Pharaoh at the palace; God is intercepting him at the exact site of his secret religious anxiety. The rod — the one that had just become a basilisk — is to be held visibly in Moses' hand. The man who reads river-signs is about to be handed a river-sign he cannot misread.
The takeaway is clarifying. Idolaters often know their gods are hollow; that is why they have to check every morning. When the real God arrives, He meets them at the dock, not at the throne.