Go Tell the Spartans

Major Asa Barker (Burt Lancaster) has been given this command: a poorly-manned outpost over seeing three villages named Boo Jum, Mung Tau &amp; Hat Song and he is ordered to re-occupy a nearby, deserted hamlet named Muc Wa in rural South Vietnam somewhere near the rural Da Nang to Phnom Penh (Cambodia) highway that a decade earlier had been the scene of a massacre of French soldiers during the First Indochina War. Barker is a weary infantry veteran in his third war (he served in the Pacific during World War II as well as in the Korean War), who provides veteran supervision to a cadre of advisors attached to a group of South Vietnamese who are ordered to garrison the deserted hamlet of Muc Wa.[2]
Major Barker and his executive officer, the career orientated Captain Olivetti receive four replacements. Second Lieutenant Hamilton has been passed over for promotion and sees volunteering for Vietnam is a way to obtain a promotion to remain in the Army. First Sergeant Oleozewski served in the Korean War under Major Barker and is burnt out fromthree tours in Vietnam; his last assignment saw his previous unit massacred. Cpl Abraham Lincoln is a combat medic and a drug addict. The mystery to Major Barker is the fourth man, the draftee Cpl. Courcey, a demolitions expert who extended his enlistment by six months to serve in Vietnam. Major Barker sends his four new men plus Cpl. Ackley, a communications expert to garrison Muc Wa with a half French half Vietnamese interpreter/interrogation specialist called Cowboy, a hardcore squad of Nung mercenaries and a motley mob of about 30 South Vietnamese Popular Force civilian "troops" armed with shotguns and old rifles with a sprinkling of machine guns attempt to create a defensible outpost at Muc Wa.
On their way to Muc Wa along a dirt road, the column is ambushed at a roadblock, resulting in the overly enthusiastic Cowboy capturing and beheading the lone Viet Cong attacker. On reaching the hamlet, Hamilton sets up his defenses in a triangular formation and receives supplies brought in by helicopter. At the rear of the hamlet is a graveyard of 302 French soldiers, massacred in a VC attack ten years earlier immortalized with a placard above the entrance that reads, in French, "Ãtrangers, dites aux Spartiates que nous demeurons ici par obÃ©issance Ã  leurs lois" ('Foreigners, tell the Spartans that we remain here, in obedience to their laws"), which refers to the Battle of Thermopylae. While he is investigating it, Courcey spots a one-eyed VC soldier, who is presumably a scout.
During a patrol, Courcey spots a group of nine Vietnamese women and children fishing along the small river that runs through the deserted Muc Wa village, despite intelligence that there are no civilians said to live in the area.
That evening, the VC attack Muc Wa with a harassing attack where the doped up Lincoln is wounded. Courcey leads an ambush patrol that kills the four Viet Cong mortar crew.
The next morning, Barker travels to Saigon to meet with Colonel Minh, the military chief of the region where he tries to persuade him to send reinforcements of at least 300 ARVN troops to Muc Wa. But the corrupt Minh refuses for he claims that he needs the troops to stay in Saigon to prevent a potential coup that may happen.After some reassurance and finagling of Colonel Minh the Vietnamese Colonel informs, Baker that the requested troops will be released in exchange for 1,500 155mm howitzer shells.
That evening the outpost is attacked and Lt. Hamilton is killed as he tries to rescue a wounded militiaman, along with a few South Vietnamese soldiers. The next day, Sgt 0leonozski commits suicide rather than face the pressure of command. When Barker is informed of the deaths, he wants to pull his troops out now that they lack an experienced leader, but this request is refused by Gen. Harnitz, forcing Barker to send his own deputy to Muc Wa.
That night, the outpost is attacked again by massive numbers of Viet Cong who number in the many thousands, not the few hundred predicted by high command, and they are all well armed with various automatic weapons, as opposed to outdated rifles. Barker is forced to threaten Harnitz over the radio to send air support for Muc Wa in which several helicopters and flare ships arrive just in time to stop the Viet Cong attack.
The following morning, Barker receives orders from Harnitz to withdraw all of the American troops from Muc Wa, which is believed to be soon besieged by the 1,000-strong 507th Viet Cong battalion. Barker personally flies out to Muc Wa to evacuate the surviving Americans as well as the wounded by helicopter, but leaving behind the South Vietnamese troops, and due to mechanical issues with the helicopter, the walking wounded. The idealistic Courcey refuses to leave the wounded, so Barker decides to stays behind to help evacuate the remaining South Vietnamese troops and militiamen overland to safety. This leaves Barker, Courcey, Cowboy, the Old Man and his fellow South Vietnamese militiamen alone at Muc Wa.
The Vietnamese civilians that Courcey found and brought into the base camp steal several weapons and try to escape, forcing Cowboy to kill all of them. But the Vietnamese teenage girl gets away and informs the Viet Cong scouts of the Americans plans to withdraw... thus revealing that she and all of the other civilians were in fact Viet Cong supporters (as Cowboy predicted) after all.
That evening, Barker and Courcey are forced to destroy all of the arms and equipment left behind and then leads the group on the road departing the village, as friendly artillery fire begins raining down on the area. But no sooner has the group filed out, they are ambushed and surrounded by the Viet Cong, led by the civilian girl.
The only survivor of the final battle is ironically the willing volunteer, Courcey, whose idealism and enthusiasm for the Vietnam War has now been killed along with all his comrades. He wakes up in the morning to find that everyone else is dead and the soldiers, including Barker, are stripped of their fatigues. The VC have withdrawn having left him for dead. As Courcey wanders to the grave site, he finds another survivor: the wounded, one-eyed VC scout that he saw earlier. The VC points his rifle at Courcey before dropping it out of exhaustion. Courcey says to the one-eyed VC, "I'm going home, Charlie, if they'll let me" as he wanders off the grave site and onto the dirt road leading away from the ruins of the village. The film closes with the title card which reads '1964'.

Question: Who decides to stays behind to help?
Answer: Barker