The position of the S. Vietnamese was an increasingly tenuous one. They obviously could see the war was not going well and the support of the US was waning. Other than make demands of the US during negotiations, as you mentioned, what was the S. Vietnamese reaction to the US desire to save face?
The South Vietnamese understood fairly quickly in the negotiations that they stood to be the biggest losers. The United States, under mounting domestic pressure, were able to save face with a withdrawal. The North Vietnamese, also facing significant drop in public support, were able to claim a level of victory out of the negotiations.
Yet, the South Vietnamese were in a tough position. The South Vietnamese reaction to the United States' desire to save face was to recognize its few options. It could not beat the North Vietnamese on the battlefield without American troops. Even with the Americans leaving their machinery behind to the South Vietnamese, the South understood that it could not compete. Adding to this was that the political leadership of the South was nowhere near as unified as in the North. General Thieu understood that he was not very popular and that the war, for better or worse, legitimatized his rule. He understood that with the US withdrawal, he would have to fend for himself politically, something he understood that he could not do.
The most overwhelming reaction that the South Vietnamese had to the United States' desire to save face was to sign the cease fire, "but secretly hope that it would fall apart in a quick time frame." This would reengage US forces and resume the fighting and Status Quo. Failing to incorporate how vastly unpopular the war was in the US domestic realm, this reaction was the only one that the South Vietnamese leadership could muster in the hopes of continuing the Status Quo when few others wished to do so.