En route to Saudi Arabia in his presidential jetliner last week, Zbigniew Brzezinski teased reporters with a handwritten note marked "Zbig, eyes only" and then told them the plane had just been buzzed by an Iranian jet fighter.

The other plane, the reporters learned later after they had filed stories based on a glimpse of the note, was in fact an American fighter. Brzezinski and reporters had rushed to judgment on the basis of a bad report.

But waving the "eyes only" note was pure Brzezinski, typical of the freewheeling style in which President Carter's national security adviser conducts his global diplomatic missions and the difficulty that others have in understanding immediately what he is up to.

Brzezinski usually shares little of the substantive part of his job with reporters, but is always glad to show items like the note on the "iranian" jet to demonstrate his own sense of his importance and derring-do in taking on the world's villains.

With Brzezinski, however, the apparent pranks and boyish enthusiasm he shows on his forays abroad often add up to significant indicators of the policy lines that lie ahead -- as was the case in May, 1978, when he dashed to the top of the Great Wall of China and looked about for a Russian "polar bear" to combat with his Chinese hosts. Seven months later, Washington suddenly normalized relations with Peking.

A similar venture into walking the thin line between humor and an international gaffe occurred on last week's trip to Pakistan and Saudi Arabia. Posing in the Khyber Pass, Brzezinski told onlookers: "This is a historic picture -- taken just three weeks before the march on Kabul."

The Soviet invasion of Afghanistan had brought Brzezinski to Pakistan, and any apprehension in Moscow about American-inspired efforts to take Soviet troops on militarily in Afghanistan could only have been intensified by his joke.

Brzezinski and his aides clearly relished leaving Washington and getting to the Afghan-Pakistani border -- the front line of the latest U.S. Soviet confrontation.

The Symbolic visit to the front lines was obviously as important a part of Brzezinski's trip as the substantive talks he and Deputy Secretary of State Warren Christopher held over two days with Pakistani President Mohammad Zia ul-Hag.

It appeared at times as if Brzezinski concentrated more on the symbolic than the substantive, the circus rather than the bread. He stayed in the Khyber Pass until late in the afternoon, arriving back at Islamabad shortly before his final talks with Zia were to start. He refused to cut the trip short when fog prevented his helicopter from going to the officer's mess of the Khyber Rifles. Instead, he insisted on making the trip by road rather than returning early to bone up for the talks.

Brzezinski's boyish exuberance appeared to get the best of him at an advance Pakistani outpost in the Khyber Pass, where he romped through an inspection of the Khyber Rifles' weapons. He hesitated when invited to fire a burst from a light machine gun in the direction of Soviet Forces beyond the Afghan border, two miles away, but he encouraged the Pakistani soldier to do so.

But Brzezinski refrained from that type of romping at an Afghan refugee camp, where men pleaded for arms to help them free their country. Brzezinski was careful to encourage their opposition to the Soviet takeover without promising military aid.

But he was disappointed to learn that security forces had taken away the refugees' weapons so they could not give the traditional sign of approval of his statement -- the firing of rifles into the air.

At the same time, there was a casual, laid-back side to the trip. No thick briefing books were evident on his plane and he did not appear to huddle with assistants to go over the latest position papers for meetings.

An aide said Brzezinski doesn't need last-minute cramming.

Traveling with Brzezinski was a far more pleasant experience than similar trips with his predecessor, Henry Kissinger.

Gone were the security guards that Kissinger liked.

Brzezinski spent a good part of the flight playing chess with a reporter in the back of the plane. He clearly likes the press, some say even better than he likes the State Department experts who travel with him.