President Reagan's signing July 17 of a law pressuring states to raise the legal drinking age to 21 is the latest move to get young, drinking drivers off the the nation's highways. But it's not likely to be the last.Driving curfews may be down the road for many of America's teen-age drivers.Support for limits on late-night driving by youths under 18 appears to be building among state legislators and highway safety activists. There also is substantial opposition.Twelve states have laws restricting the hours during which certain teen-agers can drive.Under Louisiana law drivers under 17 must be off the roads from 11 p.m. to 5 a.m. In New York all 16- and 17-year-olds who have not had driver-education courses, are forbidden to operate a motor vehicle between 9 p.m. and 5 a.m. Massachusetts does not allow drivers under 18 to be behind the wheel between 1 a.m. and 5 a.m. Illinois, Indiana, Maryland, Michigan, Pennsylvania, South Carolina, South Dakota, Wisconsin, and Wyoming also have some type of curfew for certain teen-age drivers.Federal legislation signed by President Reagan gives individual states two years to raise the legal drinking age to 21 or face withholding of up to 15 percent of their highway construction and road repair funds from Uncle Sam over the following 24 months. This measure, based substantially on recommendations of the President's Commission on Drunk Driving, is expected to reduce perhaps substantially, the number of liquor-related motor vehicle accidents involving 18- to 20-year-old drivers.The presidential commission, chaired by former Massachusetts Gov. John A. Volpe, considered a curfew for teen-agers among alternatives for reducing highway crashes. Mr. Volpe now says he is ''not opposed to the idea,'' but he questions ''how well it would be enforced.''Proponents of curfews are encouraged by a survey that indicates young people may actually support such restrictions. Some 50,000 high school students in seven states completed questionnaires for a study team of the Washington, D.C.-based Insurance Institute for Highway Safety (IIHS). The study team concludes that ''teen-agers do, to some extent, favor - or at least do not oppose - laws that would restrict teen-age driving.'' Ninety percent of the students surveyed in New York and Louisiana, two of the states with curfew laws, favored the restrictions.More than half the survey participants in noncurfew states ''chose a starting time'' for youthful drivers to be off the road. This is interpreted by IIHS analysts as an indication these respondents ''do not oppose a curfew.''Curfew proposals have been discussed recently in several legislatures from New England to the West Coast.In 1983 such a proposal came within four votes of making it through the California Assembly. Earlier this year a watered-down version of the measure made it through the Assembly only to be defeated in the state Senate. Its sponsor, Assemblyman Alister McAlister (D) of Fremont, says that despite ''stiff legislative opposition'' there is ''strong public support'' for a curfew.In Massachusetts, state Sen. Louis Bertonazzi (D) of Milford plans next year to file legislation that would raise from 16 1/2 to 17 1/2 the minimum age for obtaining a driver's license and extend by three hours the current curfew for motorists under 18. Instead of 1 a.m. young drivers would have to be off the road by 10 p.m. The IIHS, noting that 16- to 19-year-olds make up less than 10 percent of the nation's population yet account for 17 percent of all motor vehicle fatalities, emphasizes that teen-age drivers are ''far more likely to be 'at fault' in fatal crashes'' than those in higher age groups. And the number of road fatalities in which youthful drivers are involved, especially in nighttime hours, is five times that for motorists aged 35 to 64, IIHS researchers observe.Dr. Allan Williams, the IIHS researcher who headed the study team, acknowledges that no law restricting youth driving is apt to be popular with with those affected. But he views the night driving curfew as ''more acceptable (among teens) than raising the drinking age.''The potential effectiveness of nighttime teen-age driving restrictions is underscored by a 1983 IIHS study that indicated 69 percent fewer nighttime crashes involving teen-agers in New York than would have occurred without a curfew.Pennsylvania's curfew for 16- and 17-year-olds, which runs from midnight to 5 a.m. was credited with preventing crashes involving youths in that age group by 62 percent. A reduction of 40 percent in nighttime crashes by drivers under 18 between 1 a.m. and 6 a.m. was noted in Maryland after 1978, when the state curfew law went on the books. And Louisiana officials estimated that 15 percent fewer youth-involved crashes occurred than might have without the 11 p.m. to 5 a.m. curfew on motorists under 17.