See how Philip Habib runs -- from Beirut to Jerusalem to Damascus to the Saudi Arabian capital of Riyadh. What you may be seeing in the peregrinations of the special presidential envoy for the Lebanese "missile crisis" is a preview of how the door to a wider settlement of the Arab-Israeli conflict could someday be unlocked.

The key would be Saudi Arabia, bankroller at one time or another for just about all the forces at work in the Arab world. The Saudis funnel untold millions of dollars to the Palestine Liveration Organization. They gave or lend openly to governments and covertly to opposition movements when it suits their purposes.

They are the principal financiers of the $1.8 billion "steadfastness fund" created to shore up Syria and other of the Arab states bordering on Israel. With Kuwait, they had been paying for the Syrian "Arab peace force" in Lebanon until recently, when the Syrians apparently were late filing their expense accounts.

It is the Saudi financial connection with Syria, and the influence it can presumably buy, that drew Habib to Riyadh. That same connection, it is said, enabled the Saudis to cool (or perhaps to buy) off a Syrian threat to Jordan last fall.

Whether Saudi Arabia can contribute to comparable results in the crisis created by Syrian deployment of SAM6 ground-to-air missiles in Lebanon's Bekaa Valley is uncertain. It may never be clear, because face-saving is the name of the game Habib is playing.

But what seems likely to happen is that a loose -- and quite possibly not fully acknowledged -- bargain will be struck. It would consist of redeployments of assorted military forces -- Syrian, Lebanese and Israeli -- that have all but stripped Lebanon of its sovereignty and turned its territory into a sort of military/political proving ground.

Hter would be new, perhaps unwritten, rules jof engagement for the regular Lebanese government forces, the rightwing Lebanese Christian militia, the Syrian occupiers in the name of "peace," and the occasional Israeli invaders-by-air against PLO camps and in support of the right-wing Christian minority.

But somewhere in any package, I suspect there will be a Saudi incentive for Syria's canny, inconstant President Hafez Assad, perhaps in the form of a resumption of the payments for the Syrian occupation force in Lebannon.

That's if all goes well -- if the Israelis don't finally try to take out the missiles and the Syrians don't retaliate in a way that could blow up into a wider war. But even if all goes as well as can be expected, Lebanon will remain a dangerously incendiary cockpit of Arab-Israeli strife over the central Palestinian issue.

And something of consequance will have been lost. By its various entreaties to the Soviets to restrain the Syrians, the Reagan administration has measurably strengthened Moscow's claim to a continuing role in the Middle East peace-making process. U.S. policy has been to freeze the Soviets out, with one notable exception: the joint U.S.-Soviet declaration worked out by the Carter administration in 1977 and loudly denounced by Ronald Reagan in last year's presidential campaign.

To the extent that the soviets now have a foot back in the door, it will be an urgent imperative of the reagan administration to dislodge it. And the best way to do that would be somehow to break or at least loosen soviet ties to Syria.

How?We come back to the longer range potential of Saudi influence on Syria, whose Soviet connection was tightened last October by a formal treaty of "friendship" with Moscow. One effect of this was the hieghten concern among Arab "moderates" (Saudi Arabia, Jordan, even Iraw) over the expanding Soviet "persence" in the area. The result has been increased isolation of Syria, a drying up of investment and outside support and severe economic difficulties.

Assad also faces opposition from Syria's Sunni Moslem majority. In the opinion of knowledgeable authorities, Saudi money could ease Assad's economic problems, and his political problems as well. With the right touch, the United States could even help encourage a gradual weaning away of Syria from the Soviets and, in the process, advance the "peace process." The recent teetering on the brink of renewed Arab-Israeli warfare -- or even a harrowing superpower confrontation over Lebanon -- adds force to the argument for getting on with some variation of the Camp David "framework." Support fromthe moderate Arabs is a must.

The stage may soon be set for a big and infinitely intricate U.S. diplomatic initiative. Serious concessions will be called for all around -- from Israel, and from the Saudis in exchange for AWACS and other armaments. More will be required than merely seeking a "strategic consensus" for defense of the Persian Gulf.

But the lesson of the Lebanese missile crisis is that the Soviets can extend their influence in the Middle East by ways other that an outright grab for Gulf oil.