In short: not very. It wasn't what we would consider "unconditional" and was certainly with a bit of reluctance. Eisenhower and Truman felt that Park's predecessor, Rhee, was encouraging further military engagement with South Korea as a first step of reopening the Korean War and "finishing" unification to the point where there was a plan in place to topple his regime should he antagonize the North too much or act as too much of a hindrance to armistice. The spectre of "wanted to defend an ally but not antagonize the North (and thus China and the Soviets)" is a common thread in a lot of of the post-Korean War interactions between the US and the ROK. They were also reluctant to give much public support to the regime due to the fact that it was, at times, just as dictatorial and abusive to its people as the Kims were to the north.
When Park overthrew the transitional government after Rhee, the US seemed less interested in supporting the still-dictatorial South (as China and the Soviets were doing in the North) than it was with pursuing relations with China, a state that was one of the patrons of the North. When Nixon announced that he was visiting China, the South Koreans demanded a summit prior to that and Nixon said no. Nixon's "Guam Doctrine" also saw massive withdrawals of US troops from South Korea and basically stated that the US would help defend the "free states" of the world, but the onus was on those states to provide the bulk of the manpower. Following Vietnam, the American public support for intervention in Korea on the event of North Korean aggression hit it's lowest point: after the fall of Saigon, only 14% of Americans responded favorably to the idea. A full 65% said they opposed the idea.
After Vietnam, normalizing relations with China, and the scandal of South Korean interests bribing US Congressmen, US support for South Korea was at its nadir. President Carter went even further and campaigned on the idea of complete removal of US troops from the penninsula and proposed a phased withdrawal plan which resulted in the removal of all troops and weapons by 1982. Carter believed that the presence of the troops exacerbated the tensions between the two Koreas and that removal would "spur the South Koreans to pursue autonomous self-defense capabilities, and would incentivize the two Koreas to sign a peace treaty." Carter's reluctance to continue to support the South came from Park's oppressive rule: "It should be made clear," he said in a 1976 speech, "to the South Korean government that its internal oppression is repugnant to our people and undermines the support of our commitment there." After it was revealed the Park was working with the French to obtain nuclear capabilities, "Donald Rumsfeld (then Secretary of Defense) bluntly threated in 1976 that Washington would consider severing the entire relationship unless Seoul canceled the contract with France."
Unfortunately, most of my reading is in the context of North Korea's history and the Korean War, so I don't have much I can offer on the relationship between the Americans and Chun Doo-hwan.
(Most of this was sourced from The Impossible State: North Korea, Past and Future by Victor Cha, as well as from Under the Loving Care of the Fatherly Leader, by Bradley Martin.)