The instant the last Senate vote is cast in the Bork battle President Reagan should demonstrate political vigor by nominating J. Harvie Wilkinson III to the Supreme Court.

Judge Wilkinson, 43, is on the U.S. Fourth Circuit Court of Appeals in Richmond, a court once adorned by John Marshall. He is a former clerk for, and something of a disciple of, the justice whose place he would take, Lewis Powell, whom many of Robert Bork's critics say they revere.

Wilkinson has been a professor at the University of Virginia law school. He was deputy assistant attorney general in the Civil Rights Division in 1982-83. He has written significant opinions on the circuit court, as well as subtle jurisprudential analyses.

The politics of a Wilkinson nomination would be satisfying. Some southern senators cleave to the retrograde idea that there should be a ''southern seat.'' Southerners are not, alas, uniquely perverse. Others have embraced the idea of a ''Jewish seat'' and a ''black seat.'' Reagan's contribution to this spoils-system mentality was a 1980 pledge to nominate someone because of her chromosomes.

Nevertheless, it would be entertaining to watch the Kennedy-Metzenbaum-Biden faction trying to enlist southern Democrats in a second mugging of a nominee, this time one from Virginia. Furthermore, a Wilkinson nomination would force moderate Democrats to decide if they want to enter 1988 with Kennedy, Metzenbaum and Biden defining their party in a scorched-earth insistence on a Supreme Court obedient to their catechism.

When, in 1984, the Senate confirmed Wilkinson for his current position, the vote was 58 to 39, with the outlines of the anti-Bork faction in place. This fact might cause Reagan to flinch from a Wilkinson nomination, or it might rouse him to a fight -- if the White House has any fight left in it.

Some opposition to Wilkinson arose because, when he was apprised of the fact that there were doubts about his qualifications on the part of some members of the American Bar Association screening committee, he asked a few friends to contact some committee members and affirm his qualifications. Kennedy announced himself scandalized by this mild intrusion of politicking into the confirmation process. (Kennedy recovered from his attack of fastidiousness in time to orchestrate the national campaign against Bork.)

There is one indelible blot on Wilkinson's escutcheon. For three years he sank to journalism, as editor of the Norfolk Virginian-Pilot. But the limited ABA opposition (the screening committee ranked him qualified) arose primarily from the fact that he has never practiced law. Lack of litigation experience might be a significant defect in a trial judge. However, the appellate bench demands different attributes, including learnedness concerning jurisprudence and a reflective bent, both of which Wilkinson possesses amply.

In ''From Brown to Bakke: The Supreme Court and School Integration, 1954-1978,'' Wilkinson provides a masterful jurisprudential and sociological analysis of the ''maturing journey'' from ''optimism and confidence to confusion and doubts.'' There has been an explosive melding of two perennial subjects that arouse American passions -- race and public education. This, Wilkinson says, has illuminated the court's dilemma as ''an institution protecting minority rights in a nation of majority rule. Its members feel not just their special obligation to protect minorities but the lurking inconsistencies of judicial activism with democratic notions of self-governance.''

In his book, he demonstrates a lively awareness of both the emotional pull toward, and the reasons for being wary of, programs of ''compensatory justice.'' And in an opinion written this July, in a case concerning a ''minority set-aside'' program for contractors on Richmond construction projects, he demonstrated how carefully circumscribed ''race-conscious remedies'' (affirmative action) must be if they are to comport with the Constitution's equal-protection guarantees.

His analysis was foreshadowed in a 1975 Virginia Law Review article, ''The Supreme Court, the Equal Protection Clause and the Three Faces of Constitutional Equality.'' The ''three faces'' are equality of political participation, of competitive opportunity and of economic and material conditions.

Wilkinson approvingly cited Justice John Harlan's 1967 warning that ''newly contrived constitutional rights have been established without any apparent concern for the empirical process that goes with legislative reform.'' And in urging courts to show restraint in order to accord proper scope to the exercise of political authority, Wilkinson said, ''I cannot do better than to quote'' an eminent law professor who has urged courts to restrain themselves lest legislatures' rights be unduly abridged. That professor wrote: ''The existence of close cases is not a reason to refuse to draw a line and so deny majorities the power to govern in areas where their power is legitimate.''

So wrote Robert Bork.