Well, prior to October 13th there wasn't much reason for a ceasefire. While Syria had been pressing for one because of its weakness and the potential threat to Damascus, there was definitely a sense that Egyptian advances that had until then gone over fairly well could relieve enough pressure on Syria to continue the war.

This calculus began to be reversed by October 13, after the disastrous Egyptian advance beyond their air-defense systems. Israel had been uncertain about its ability to continue the war, needing resupply from the US (which began to arrive) just to continue servicing weaponry on the western flank, and Egypt felt that they had Israel on the ropes. There was no reason for them to accept a ceasefire right then, because of the momentum.

Sadat's goal was not to take just a sliver of land on the eastern Suez, and the unwillingness of Israel to withdraw to pre-1967 borders (as the book you linked notes) meant that Sadat would not have achieved the rather muted goal he sought. Coming back to his people with less than pre-1967 borders would be enough to meet his pledges, but coming back with even less than that, when the Arab world had once aimed to destroy Israel outright, would likely be politically dangerous.

Once the failed offensive October 13 occurred, the Egyptians began to have some doubts. But it was not until around October 19 that they seriously sought a ceasefire. Until then, the Egyptian army had held out hope of recovery, but Israel was continuously pushing them back. Sadat was actually asked why his change of heart happened in terms of seeking a ceasefire. He described a visit to Center Ten, the Egyptian Operations Command, which he said convinced him that Egypt's forces were in grave danger and at risk of collapse. The possibility of Israel destroying the Third Army and retaking the eastern bank of the Suez was catastrophic for Sadat. If coming home with a little land at a time when he had the momentum would be dangerous, the idea that he would come to his people with absolutely nothing for this war and all its devastation, along with a destroyed Third Army, was political suicide. The ceasefire lines were unfavorable enough as it was, after all.

Sadat's rejection of the ceasefire around October 12/13 partially resulted from not even knowing the tide was turning. He didn't know the scale of the American airlift to Israel, he felt strong still with the early victories, the Soviet airlift was continuing, and there was no reason to stop at a moment of strength when he felt he could dictate the result. Ismail Fahmy, the Foreign Minister, was actually upset at Sadat's rejection of ceasefire. He later wrote that Sadat was overly confident, that Assad assured him Syria had no problem, and that Israel would "continue to violate the ceasefire anyways". Fahmy wrote that he responded that Israel might do so, but better that they do it on the east bank of the Suez than that they manage to cross it. This prediction proved correct: both sides violated the ceasefire when it came about, and Israel did threaten to cross the Suez, and did cross it to encircle the Third Army.