For thousands of Haitians, the way to America had the simple allure of a Madison Avenue advertisement: follow the sun.

And so they did. Fleeing poverty and tyranny, they boarded open boats and journeyed the 800 miles to the Florida shores.

"They asked someone, 'How do we get to the United States?" said Fr. Gerard Jean-Juste, director of the Haitian Refugee Center here. "They were told, 'On the morning, the sun's rays come from Haiti. At night, they go to the United States. Just follow the sun . . .'"

What they found was a nightmare. Some were jailed, some swiftly deported. But most of them have melted into south Florida's black ghettoes, where they try to survive without government assistance, without the legal right to work and constantly facing the threat of deportation.

The Haitian migration began in the early 1960s, about the same time the Cubans started arriving and more than a decade before the influx of an estimated 176,000 Indochinese fleeing the upheavals caused by the fall of South Vietnam in 1975.

Few people paid attention when the Haitian boats began coming ashore. Fewer still paid heed to Haitian claims that they were, and are, political refugees seeking freedom in the United States.

But now, in the wake of President Carter's human rights campaign and in reaction to attention given the Indochinese boat people, the case of the Haitian refugees has taken on new inpact.

The Haitians sense this. They have increased their marches and demonstrations in Miami, stepped up their criticism of the Haitian government and worked with their lawyers to wage a full-scale legal battle against deportation proceedings. In short, they have started a new civil rights movement in south Florida,

Estimates of the number of Haitians living in south Florida range from 10,000 to 23,000. Between 3,000 and 5,000 live and work in the Palm Beach County town of Belle Glade-a blotch of urban blight in the midst of sugar cane and corn fields 76 miles northwest of Miami.

It is a curious life made all the more curious by the Haitian boat peoples' doubtful legal status, by their "certain kind of invisibility," according to Joseph Occhipinti, manager of the state employment office in Belle Glade.

"Most of the Haitians are without work permits, can't get work permits and are not supposed to work," Occhipinti said.

"But the corn fields around here couldn't be picked without the illegal Haitian-and they sure are being picked.

"So, I guess I have to tell you that the corn fields are being picked by nobody . . . It's a kind of slavery, but we don't have much control over it."

No one argues that the Haitians have not been treated differently than the Cubans or the Indochinese.

The Haitian boat people and their supporters say they are political refugees, entitled to the same federal protections and privileges given the 32,000 Hungarian refugees who fled communist oppression between 1956 and 1958, the 260,000 Cuban refugees who ran from Fidel Castro's regime between 1965 and 1973, and the masses of Indochinese who more recently fled to the United States.

The Haitian boat people say they are running from similar tyranny under the dictatorship of Haitian President-for-life Jean Claude Duvalier.

"We did not come to your country for food or money," declared Kenol Luxama, 27, a former newspaper reporter in Port Au Prince, Haiti.

"We came here thinking that we would get human rights in spite of the American support of the Duvalier regime," he said.

"But the things the American government has for us are jail and bail from the charities to get us out of jail . . . What makes the Americans think we want their oppression more than we want Duvalier's oppression?All we want is our freedom," Luxama said.

The U.S. Immigration and Naturalization Service disagree.

Most of the Haitians are economic refugees, having a status "no different than that of the illegal Mexican alien who crosses the border on foot," said Deputy INS Commissioner Mario Noto, Whose name is greeted with cynicism in south Florida's Haitian communities.

Current federal law defines refugees as persons fleeing communism or the Middle East, Noto pointed out, and Congress enacted special programs to help the Cubans and Indochinese.

The Haitians lose on all counts, Noto said.

Accordingly, INS policy has been to jail Haitians arriving "without papers" and without funds to post bonds ranging up to $1,000.

In one instance last year, authorities "mistakenly" jailed an 8-year-old girl, Roselene Dorsainvil, who came ashore with her father. She was in the West Palm Beach City Jail with adult inmates for about two weeks.

The Dorsainvil incident was roundly denounced by church, civil and human rights groups.

Of the nearly 9,000 Haitians in south Florida now subject to deportation, about 3,200 have formally applied for political asylum since 1972, and more are applying every day. INS has approved 58 of the applications and has rejected nearly all of the rest.

The mass asylum rejections, the jailings and the "voluntary deportations" of hundreds of Haitians formed the basis for a federal lawsuit filed here last week on the Haitians' behalf.

The suit-entered by the Washington-based Lawyers' Committee for Civil Rights Under Law-alleges that the Haitians were denied due process from the moment of their arrival and singled out for special adversary action largely because they are black, poor and illiterate.

The racism charge was denounced by Noto as a "hurtful . . . unwarranted perception."

But it is a perception that persists, and the suit, accordingly, asks that INS reconsider all of the Haitian political asylum applications on grounds they were handled in a biased manner. The suit also asks the court to enjoin INS from deporting any other Haitians here seeking refuge.

The Haitian plight has touched a sensitive nerve in the south Florida area, particularly in sprawling Dade County, where hundreds of thousands of whites, Cubans and American blacks already are engaged in a struggle for economic and political power.

Fifty percent of Dade County's 1.53 million inhabitants are white, 35 percent Hispanic and 15 percent black.

Though many of the Haitian newcomers have been absorbed into the county's predominantly black northwest neighborhoods, they are not entirely welcome there. Their distinctive French Creole language, their tendency shared by most refugee groups to stick together, and their insistence on anonymity work to isolate them from many of their black American neighbors.

Still, there are indications that things are changing in the Haitians' favors. Recent demonstrations here for Haitian refugee rights have attracted outpourings of native black support, a significant white presence and some support from Cuban socialist groups.

The Carter administration has introduced legislation to broaden the federal definition of "refugee."

The Senate Foreign Relations Committee voted May 3 to cancel $18.4 million in U.S aid to the Duvalier government on grounds that it has failed to implement fiscal reforms and clean up alleged rampant corruption. Haitian boat people and their supporters saw the vote as an endorsement of their view that economic disorder in Haiti is spawned by political oppression.

Rep. William Lehman (D-Fla.), a member of the House Appropriations subcommitted on foreign operations, took a trip to Haiti last month to assess conditions there. The State Department is now conducting a similar study.

Upon returning from his trip, Lehman said he believes the Haitians have been treated unfairly here.

"In a country that believes in human rights, that just ain't the way things ought to be done," the congressman said.