realised we forgot Lebanon, so:
October 14-16, 1981: Believing the PLO will start up operations across the Lebanese border at any moment and since the IDF are already at full mobilisation, Israel launches air raids for three days on PLO positions. Bush and Baker are able to talk Begin into stopping this, with Egyptian brokers reaching out between Israel and the PLO under Sadat's orders - Begin doesn't want too long a war and accepts another informal deal. Defence Minister Arial Sharon, riding high, is unhappy with this and starts internal pressure to go in and not just remove the PLO, but perform regime change in Lebanon.
April 2nd to 12th, 1982: Strikes and rioting in the West Bank, which spread sporadically in Gaza. Gunmen open fire on Israeli soldiers on the 5th, 6th, and 10th, which Sharon uses to claim that the PLO are behind this and action is needed in Lebanon. This is passed on to the US, where Baker advises that Israel could succeed in installing a new government but only bring extra nations into the civil war. Bush orders Nixon to begin talking to the Soviets about Lebanon, on the theme that neither of them want "another" problem in the region.
April 14th-16th, 1982: America proposes a UN peacekeeping force in Lebanon, as part of a broad ceasefire agreement before upcoming elections - the US Marines will contribute a lion's share of the personel. In what's assumed at the time to be the Soviet's keeping their hand in (but is actually part of Nixon's deal), the USSR supports this and says Azerbaijin Soviet soldiers will be sent too. In Lebanon, the US quietly informs President Sarkis that Israel may attack and that it's in his best interests to cut deals; peace talks are hastily begun under UN supervision and Sarkis reaches out to Amal leader Nabih Berri and Christian leader Bashir Gemayel. Rashid Karami is made PM again.
April 17th, 1982: Sharon is forbidden to attack Lebanon before the peace deal - Begin assumes they may need to go to war later but wants the political cover of the UN failing first. To Begin's outrage, Sharon resigns, publicly calls Begin's leadership into question (including saying "the Baathists are still in Bahgdad"), and implies he'll challenge his leadership in the right-wing coalition.
April 29th, 1982: Multinational Force in Lebanon arrives, with US, Soviet, French, Egyptian, and Turkish soldiers (the Turkish military regime wanting to show off domestically and Egypt wants to be sure hold off Israel & one-up Syria). A very shaky national government has formed but the bulk of the militias have not agreed to stand down, and peacekeepers are shot at early.
May 2nd, 1982: Sharon's leadership challenge fails: Begin had managed to talk enough people in the coalition into supporting him over Sharon, using the defeat of Saddam Hussein as evidence he knows what he's doing and indicating Sharon is too loose a cannon. While Sharon is left in the cold and Israeli ambassadors use this to try & sell Lebanon on how Israel is 'friendly' as long as the PLO stay quiet, Begin is quietly having plans drawn up for the (to him) inevitable PLO war.
May 18th, 1982: Three US Marines on patrol are killed at a refugee camp, during a raid by Christian militias. Bush has the flags lowered at half mast. Polls show the population, relaxed about wars after Iraq, are still in favour.
June 2nd, 1982: French embassy in Beruit is bombed, killing eighteen people. Islamic Amal claims responsibility and Nabih Berri denounces it.
June 9th-10th, 1982: Attack on a nightclub popular with US Marines, killing two. Bush uses this to get Congress to approve sending arms shipments to the "legitimate government of Lebanon", who he hopes will hold off their own threats.
August 21, 1982: Elias Sarkis is re-elected President of Lebanon. (Behind his back, a disgruntled Bachir Gemayal passes on to the Israelis that he's willing to cooperate if tehy want regime change) He announces that "co-operating militias" will be merged into the army if they stand down in the next week.
October 4th-5th, 1982: US helicopter downed while on patrol over Lebanon, supporting the domestic army against remaining militias. It's clear the militias are being given weapons by Syria - the US sends a sharp warning to Damascus, including a threat that if Israel and Syria go to war again, it won't matter what pretext Israel wants to use.
September 10th, 1983: Multinational Force in Lebanon begins to stand down, including half the US Marines going home. The news sends poll approval of the intervention up to 61%: since Glen Canyon, it had been down to 40%. Behind the scenes, Baker gets approval from Sarkis to set up a permanent small Navy base on the coast.