It has been more than four decades, but Ben Barnes said he remembers it vividly. His longtime political mentor invited him on a mission to the Middle East. What Mr. Barnes said he did not realize until later was the real purpose of the mission: to sabotage the re-election campaign of the president of the United States. It was 1980 and Jimmy Carter was in the White House, bedeviled by a hostage crisis in Iran that had paralyzed his presidency and hampered his effort to win a second term. Mr. Carter's best chance for victory was to free the 52 Americans held captive before Election Day. That was something that Mr. Barnes said his mentor was determined to prevent. His mentor was John B. Connally Jr., a titan of American politics. Now Mr. Connally resolved to help Mr. Reagan beat Mr. Carter. What happened next Mr. Barnes has largely kept secret for nearly 43 years. Mr. Connally, he said, took him to one Middle Eastern capital after another that summer, meeting with a host of regional leaders to deliver a blunt message to be passed to Iran: Don't release the hostages before the election. Mr. Reagan will win and give you a better deal. Mr. Connally's files indicated that he did, in fact, leave Houston on July 18, 1980, for a trip that would take him to Jordan, Syria, Lebanon, Saudi Arabia, Egypt and Israel before returning to Houston on Aug. 11. Iran did hold the hostages until after the election, which Mr. Reagan won, and did not release them until minutes after noon on Jan. 20, 1981, when Mr. Carter left office.