Arrington Dixon is moonlighting as an insurance salesman. Marion Barry, who has a lower city salary than his finance committee clerk, says he is thinking about taking a part-time job during the City council's August recess.

John Wilson has recently quit a $10,000-a-year part-time job because, he said, he fears the news media might portray it as a conflict of interest. "Now that I'm officially broke," he complains to a reporter, "y'all should be happy."

The demands of devoting full-time efforts to what officially is a part-time job, the fringe costs of life in public office and the financial restrictions of being looked into a GS-12 salary have given members of the D. C. City Council an unexpected affinity with some of their constituents.

"We're on a fixed income," says Willie J. Hardy (D-seven), who recently bought a new $8,000 car. "I don't like being on a fixed income."

The home rule charter sets the salaries of the city's 12 regular Council members at the GS-12, step 10 level, currently $26,571 a year. The Council chairman is paid an additional $10,000 per year, under the stipulation that the chairman work full-time for the city and not hold any other salaried job.

The wisdom of that logic has been questioned during the recent debate over the financial affairs of City Council Chairman Sterling Tucker, who for the past two years made more than $15,000 working as a staff lecturer at Howard University.

Corporation Counsel John R. Risher Jr., contending that Tucker has violated his right to hold office, has asked the D.C. Superior Court to oust Tucker from office. Tucker maintains his employment at Howard had approval from the congressional leaders who drafted the home rule legislation. The court has yet to rule on Risher's petition.

Several supporters of Tucker have indicated that in spite of the intent of the law, Tucker has not slighted his full-time Council duties through his employment at Howard.

Based on examination of public financial disclosure forms filed by Council members and interviews with them, it appears that several Council members believe that the salaries now allocated to their jobs rate too low since none of their jobs are really part-time.

Many council members report putting in 60 hours to 80 hours a week. In addition, there are the extra costs of being a public official, which include everything from buying tickets to ice cream socials to buying clothes to wear at $100-a-plate dinners.

"You have to change evening dresses at least once or twice a week," one Council member said privately. "People expect their legislators to look respectable. And they expect you to buy tickets for their affairs and get very indignant if you don't."

During one typical week, recently, one City Council member got more than a half-dozen requests to buy tickets, ranging in price from $5 for a Howard Theater fund-raiser to $100 for a Congressional fund raiser.

Some tickets, like those to Redskins football games and Diplomats Soccer matches and Metropolitan Washington Board of Trade events often are free, but the nickels and dimes for the others add up, Council members say.

"I don't agree that the salary isn't adequate. It's just that the extracurricular expenses are a problem," says Wilson (D-two). "It's very difficult to maintain yourself on $26,000 and keep up the front that people expect you to keep up. In the proper context, this is not a poor man's business, period."

Few of the Council members are independently well off, most depend on their Council salary and complain of living from "pay check to pay chec." Polly Shackleton (D-three) appears to be by far the wealthiest member of the Council. She listed on her financial disclosure form for 1976 assets in excess of $500,000 and stated she earned $18,508 in dividends from trusts of which she is a beneficiary.

Until earlier this month Wilson received $10,000 a year as an associate director of the North Carolina-based National Sharecroppers Fund, which was among the largest outside incomes earned by the Council's 12 regular members. Unlike Tucker, they are not prohibited from outside employment.

Dixon (D-four), whose wife makes about $35,000-a-year as a lawyer, began selling insurance in February after checking first with the D.C. Board of Elections and Ethics to see if the job would be proper.

The major reason for the outside employment is the anticipated cost of putting his two daughters through college in 10 to 15 years, he said. "To do that, I'm going to have to put away about $4,000 a year," Dixon said.

Dixon, who has half ownership in his family's $100,000 home in northwest Washington, listed assets of $53-500 and liabilities of $58,124 in his public disclosure form.

Most of the other 12 regular Council members do not work part-time, though some do receive as much as $1,500 per year from personal appearances. Jerry A. Moore (R-at large), reported receiving $6,316 from 19th St. Baptist Church, of which he is pastor. Wilhelmina J. Rolark (D-eight), who joined the Council in January, said she still maintains her private law practice on a part-time basis.

The limitation on Council salaries also has created disparities between members of the Council and those who work for them. Both Council Secretary Robert A. Williams and General Counsel Edward B. Webb Jr. make in excess of $40,000 -- more than their boss, the $35,000-per-year. Council Chairman.

Edward M. Meyers, chief clerk of the Council's finance and revenue committee, makes $26,738, slightly more than any of the Council's regular members. City regulations permit other Council aides to be hired at a GS-13 level By next year, more than a half-dozen City Council committee clerks and executive assistants will be making more than their bosses.

"I think it's an outrage for people on the mayor's staff and on our own staff to be getting paid more than the members," said Shackleton. Most senior city department heads make about $45,000 per year.

Most Council members are placing their hopes in pending legislation due to be voted on later this year creating an independent civil service system for the city. That legislation would raise the salaries of all Council members by about $10,000 a year.