I doubt anybody can answer the question, “What was he thinking?” but there may be a clue as to the significance of Pharaoh telling Moses to get rid of the frogs “tomorrow”. At the outset, let me confess that I’ve had to go to my NLT Study Bible Notes for insights.
The magicians were able to duplicate the plague [of frogs] in some sense, but Pharaoh did not ask them to rid the land of the frogs. Instead, he begged Moses to take them away. He already knew where the real power was.
In this instance, the evidence of God’s power was not in the event per se but in the timing. God could keep the frogs alive or he could end their lives. Pharaoh needed only to say when.
The Egyptian frog-headed goddess Heqet was the goddess of birth. Frogs were thought to be sacred and were not to be killed. That’s why Pharaoh could not ask his magicians to get rid of them. He was forced to seek help from Moses. Just to rub it in a bit more, Moses told Pharaoh to set the time. That forced Pharaoh to acknowledge that his goddess was impotent and that only Moses’ LORD God had the power to rescue his people.
Bear in mind that prior to the plague of frogs the Nile had been turned to blood, making it undrinkable and killing all the fish. For seven days the Egyptians suffered, but Pharaoh took refuge in his palace and put the whole thing out of his mind (Exodus 7:23-25). Then came the plague of frogs. This time, Pharaoh couldn’t escape. The frogs invaded his palace, even into his bedroom and onto his bed (Exodus 8:3-4). No wonder he begged Moses to intervene!
Why “tomorrow” and not “right now”? Because Pharaoh had already lost a great deal of face and (possibly) wanted to be seen by his court as being in charge of events. Speculating here, but he might have been in such a rage that he needed Moses to get out of his presence so he could calm down. What Pharaoh didn’t realise, of course, was that it was the LORD God who was in charge, and by demanding the removal of the frogs “tomorrow” he was actually playing into God’s hands.
This would demonstrate that the LORD God was able, not only to get rid of the frogs on the land, but also to accomplish it at a specific, pre-determined time – a time of Pharaoh’s choosing.
Of course, there may have been another simple reason for waiting till tomorrow. It might have already been late in the day when Moses and Pharaoh met. But that’s just speculation on my part.