Unfortunately for Japan and fortunately for the U.S., Admiral Nagumo was the wrong person for the job, he was promoted to command of the Carrier Strike Force due to his seniority. He was competent but no experience with carriers (few at that time did have it). He did have enough leeway is his orders to take advantage of the situation, but was opposed to the attack in the first place. If the third strike had been launched, the U.S.S. Enterprise would have most likely been found and sunk.
A third strike would have been against the fuel farm and the PHNSY. Enterprise still would have been out to sea and Fuchida’s aircraft would have concentrated on those targets.