After five years of impatient waiting, Arlington County Board members Walter Frankland and Dorothy Grotos last week finally saw the Republicans light at the end of the school board tunnel.

Frankland and Grotos, who with Stephen H. Detwiler make up the Republican-backed majority on the five-member County Board, designated two replacements for school board members Mary Margaret Whipple and Richard Barton. In doing so, they ensured that the school board will be dominated by Republican appointed members for the first time in more than 12 years. Whipple and Barton, whose terms expire in June, were appointed by county boards on which Democratic-backed members held the majority.

But the appointments of Evelyn Reid Syphax, who runs a private day care center in Arlington, and Claude M. Hilton, a lawyer and former Arlington prosecutor, do not guarantee the school system will get the "shock treatment" Frankland has been prescribing since he was first elected in 1975. Observers also question whether the appointments will end the often bitter bickering that has characterized relations between the County Board and the school board over the past year.

"There's no reason to believe their appointments will be any more loyal or grateful than ours were," joked Ellen Bozman, one of the two Democratic-backed members of the County Board.

Syphax describes herself as an independent, and Hilton says he is a staunch Republican. However, both Syphax and Hilton have Democratic hosted fundraisers for Democratic candidates in the past. In 1974 Hilton ran for commonwealth's attorney as a Democrat in a primary against William Burroughs.

Despite those Democratic influences, Grotos, for one, has no doubts about her decision to approve the two appointments.

"A lot of people have seen the light in recent years," smiled Grotos, who nominated Syphax for the school position.

Syphax met most of the requirements Grotos outlined last month as the "ideal" school board member. She is an experienced teacher, with 20 years in Arlington schools, and has a reputation as a capable administrator. Since 1963 she has owned and operated her own day care center in Arlington, which currently has 60 students from ages 2 to 6.

"She's dedicated and detailed. If she tells me she's going to get something into our office, we know it's going to get here on time and going to be correctly done," said Elizabeth Hazel, the county child care coordinator who oversees licensing of private schools.

The appointment of Syphax, who is a member of one of Arlington's oldest and well-respected black families, also pleased the black community which has not had a representative on the school board since Frankland replaced Dr. Thomas Penn with O.U. Johansen last year.

That appointment created considerable controversy, both because of Johansen himself and because of remarks Frankland made to the press. Just after Johansen was appointed, Frankland told a reporter, "With a black on the board for the past eight years Arlington's school system has gone down." Blacks currently account for approximately 14 percent of the Arlington school population.

"I was not just picking a black," said Grotos. "I would hope our appointees would feel some kind of responsibility to work with the body that appointed them."

Although Syphax described herself as an independent, she has supported Democratic and Republican candidates in the past, including Grotos.

Hilton is more solidly Republican. His Democratic dalliance ended in 1974, he says. Since then he has been very active in Republican politics, serving as campaign manager to both Grotos and Frankland.

Current school board members openly question Hilton's qualifications for the school board seat. School board Chairman Ann Broder, wonders if he has the time required for the "part-time" job that often demands 40 hours a week.

"I'm confident I'll have the time to spend with the board," said Hilton.

Friends and colleagues predict Hilton will be an asset to the board. Henry Hudson, newly elected Arlington commonwealth's attorney, describes the 39-year-old Hilton as "able to resolve difficult problems fairly and . . . amicably."

Neither Hilton nor syphax would speculate on the most controversial issue raised by the County Board -- the immediate future of Superintendent Larry Cuban.

Frankland and Cuban have been fueding almost continually since Frankland was elected in 1975. The nadir of that relationship was reached in January when Frankland characterized the school system as deteriorating and blamed Cuban's administration for the alleged downward spiral. Frankland then called for Whipple and Barton to resign early. Detwiler supported Frankland's call and asked Cuban to resign before his contract expires in June of 1981.

"There is a natural conflict between the two boards," said school board chairman Broder this week. "They represent different interests and look out for different constituencies."

Broder also predicted that the new school board majority will find radical changes in school policy difficult to implement.

"They'll be faced with exactly the same problems the current school board is facing . . . and there are just a limited number of ways you can deal with those problems."