Behind the careful stroking of Israeli Prime Minister Menachem Begin the past few weeks, President Carter is moving toward a Camp David breakthrough to Mideast peace that belies the caveats from U.S. officials, including Jimmy Carter.

This is the essence of the Carter plan, now shaping up behind closed doors in Washington: Acceptance of the raw outlines of Begin's own plan for self-autonomy by West Bank Palestinians as the foundation for assured Arab sovereignty after five years.

Private signals have been sent to Carter by the Israeli government almost, but not quite, spelling this out. Publicly, Begin opened the door of future Arab sovereignty July 24, when Foreign Minister Moshe Dayan committed Israel to discuss the sovereignty

Begin himself will not commit Israel to Arab sovereignty over the area, but his private talks with American Jewish leaders are pointed: Start with my five-year self-rule plan; when it ends, I will year self-rule plan; when it ends, I will no longer be prime minister; the momentum of successful self-rule can only lead to full Arab sovereignty, probably in a federation with Jordan.

It is here that the design of Carter's plan comes into focus. The United States, not Israel, will act as Egyptian President Anwar Sadat's guarantor for Arab sovereignty following the five years of local self-rule; the United States will act as Israel's guarantor for West Bank security safeguards that Sadat himself agrees must extend far beyond the five years of self-rule.

This Carter plan makes a major concession to Israel by leaving out the Palestine Liberation Organization (PLO). It requires a major concession from Israel by curtailing inflammatory Jewish settlements on the West Bank.

Point 20 in Begin's Dec. 28 self-rule proposals demanded virtually unlimited new settlement during the five years. But highly placed figures in the right wing of Begin's government feared that new settlements would be forbidden or sharply curtailed by the Camp David summit.

Consequently, on Aug. 13, they leaked a secret Israeli government plan for five immediate new settlements in an effort to engineer a preemptive decision. Instead, within hours after the leak, the Begin Cabinet ordered the settlements "postponed."

Throughout this internal maneuvering in Jerusalem, the Cater administration was relatively dispassionate. That reflected the president's soft treatment of Begin, a key component of preparations for Camp David.

Until recently, any question about Israeli settlements caused a small earthquake in the White House. Settlements, according to the president and Secretary of State Cyrus Vance, were "illegal" and "an obstacle to peace." Yet, when Carter was asked about the five new settlements on Aug. 13, he replied quietly: "Well, I wish they wouldn't create any more settlements." Whatever Vance's real reaction to five new settlements, he sent Begin a courteous, lowkey massage asking only that they be "reconsidered" in view of the Camp David summit.

When Vance testified behind closed doors to the Senate Foreign Relations Committee, he strongly emphasized this fact: Whatever happens at Camp David or after, the Carter administration would never, never use military or economic aid to pressure Israel.

Soft-stroking Begin is part of the Carter plan to obtain from him absolutely necessary settlements concessions at Camp David or later, after Camp David has set guidelines for new negotiations between Israel and Egypt.

The Carter adminstration has come full circle in its psychological handling of Begin. It began with kid-glove treatment when Begin and his hard-line Likud coaliation took power in the summer of 1977.

After Sadat's memorable trip to Jerusalem, Carter was increasingly tough toward Begin. Some Carter officials even explored ways of moving Begin out of the premiership in favor of a more flexible politician. That questionable tactic not only failed; it consolidated Begin's political power in Israel and threatened a break between the United States and Israel.

Today, with new reasons to believe that Begin will come to Camp David Sept. 5 in a mood to negotiate, Carter's soft-stroking is designed to enhance that mood. He even took trouble to send Begin a birthday telegram for his 65th birthday, Aug. 16.

Not in 30 years has there been so real a prospect for breaking the Arab-Israeli deadlock. Wisely, the president is playing it down. But if - as now seems probable - the summit pays off, credit will go to Carter himself at a time when his presidency desperately needs a lift.