LOOKING back at the initial stage of the Middle East peace conference in Madrid, one fact emerges in boldface italics. The Palestinians who came to the bargaining table were very different from the gun-slinging, bomb-toting gang which the world had been taught to equate with the Palestine Liberation Organization (PLO).It was not simply a matter of personality or public image, though the contrast between Hanan Ashrawi, the Palestinian spokeswoman, and Yasser Arafat was hard to miss. The Palestinians the world saw on live television from Madrid had new priorities, a new approach, a new brief. The essence of that brief was a rational, pragmatic, and sometimes eloquent approach to coexistence with Israel. Above all, it was negotiable. It suggested that a new balance of power is taking shape within the PLO. Previously, the PLO had acted as though time were on its side - or at least could be made to work in its favor. Behind the four-year intifadah, or uprising, on the West Bank was an assumption that if life could be made prohibitively difficult for the Israelis, the government of Israel would ultimately abandon the occupation and permit the creation of a Palestinian state. The opposite happened. Though weary of the burdens of occupation, Israel in effect intensified it, moving new Jewish settlers onto the land at a pace which suggested de facto annexation rather than withdrawal. Time was clearly not on the side of the Palestinians. What lay ahead was not statehood but dispossession. Moderates in the PLO who saw the danger and were suffering from its consequences took their concerns to the leadership and lobbied for a change of direction. Then two things happened: * Arafat, the PLO chairman, blundered badly. He sided with Saddam Hussein of Iraq in the invasion of Kuwait, antagonizing major financial and diplomatic supporters of the PLO, including Saudi Arabia, Kuwait, and the Soviet Union. * United States Secretary of State James A. Baker III offered Palestinians of the West Bank and Gaza, but not the old PLO leadership, a chance to sit down with Israel in direct peace negotiations - a chance to ease, and perhaps ultimately end, the occupation. It was an offer Arafat could not require them to refuse. They accepted. And they did so essentially on Mr. Baker's terms. They agreed that the initial objective of negotiation would be autonomy for the West Bank and Gaza - that is, partial self-rule rather than immediate statehood - provided an eventual "two-state" solution (a State of Palestine side by side with a State of Israel) was not ruled out as the final goal. THIS approach, envisaged in the Camp David accords of 1978, was not inconsistent with Israel's terms for negotiation. It avoided, at least for the present, the explosive subject of exchanging "land for peace," which the Israelis say they are not willing to discuss. Israel signaled its satisfaction in several ways, notably by agreeing to negotiate autonomy with the Palestinian delegates directly, not with the joint Jordanian-Palestinian delegation. (As a fig leaf, one Jordanian could be present.) So ended years of vowing never to deal with the PLO. Something else also emerged. Deputy Israeli Foreign Minister Benjamin Netanyahu, arguably the most articulate Israeli spokesman since Abba Eban, and one who has the reputation of being a hard-liner, softened his tone so significantly as to suggest that perhaps the balance of power within the Israeli government might be shifting. Israel is a democracy, and the present right-wing coalition holds power only very tenuously. It is at least a reasonable speculation that, if negotiating with the PLO continues to be less than the unimaginable nightmare it was so long portrayed in popular Israeli mythology, Israelis may want Prime Minister Yitzak Shamir's hard-line softened. Or changed by a new government. Not all Palestinians welcome the gradualist approach to statehood. Not all Israelis want the Palestinians to have even partial self-rule. But extremists on both sides have been discredited. Their influence is visibly on the decline.