The skill of James A. Baker III as a player in the game of Republican succession was demonstrated by his inclusion in a Human Events photo spread of "conservatives in the Reagan administration" even though he is perceived as an archenemy by key figures on the right.

They view him as an archenemy because of his coolness, displayed behind the scenes, to the cutting issue of the right: supply-side tax reduction. But Human Events, the right-wing weekly, was justified in including Baker in its centerfold promotion of conservatives to high office in the Reagan administration.

In less than two months, Baker has established himself as the most accomplished politician in the White House and a major player in future games to determine the successor to Ronald Reagan. "Next to Bob Strauss," a White House colleague told us, "Baker is the best politician in town."

Like fellow Texan Robert S. Strauss, Baker managed to enter a president's inner circle after opposing his progress there. But whereas Strauss' opposition to Jimmy Carter was never formal, Baker managed campaigns against Reagan in 1976 (for Gerald R. Ford) and 1980 (for George Bush). Moreover, Baker is much closer to Reagan than Strauss ever was to Carter.

Nancy Reagan has been a principal patron of Baker, an urbane, Princeton-educated Houston lawyer, in his quick progress up from oblivion. He gained the confidence of both Reagans during the campaign when he was the first adviser to insist that the candidate should and must debate President Carter. His subsequent selection as White House chief of staff stunned the right.

Baker immediately set off on conciliation, volunteering responsibility for ensuring appointment of right-wingers in the administration's middle levels. Nor did Baker hide from the right that he was protecting it while their fellow conservatives long associated with Reagan -- including presidential counselor Edwin Meese III -- were oblivious to its interest.

Baker's first peace offering with the selection of Thomas W. Pauken, a right-leaning Dallas politician, as director of ACTION (which includes the Peace Corps). Baker then successfully supported Donald Devine, doggedly backed by conservatives to head the Office of Personnel Management, in a long struggle against Meese.

That Jim Baker was staking out ground on the right became indisputable when he maneuvered an assistant secretary of education slot for a bona fide new-right activist: the Rev. Bob Billings, former executive director of Moral Majority. Routinely passed over as too far out by Reagan's headhunters, Billings had abandoned hopes of federal office when Baker intervened.

Actually, such activity does not constitute abandonment of principles by Baker, who was rigorously conservative in his losing but impressive 1978 candidacy for attorney general of Texas. But neither Baker's campaign oratory in Texas nor his good works for deserving rightists in Washington undercuts the contention that he is riding the point in the Republican war of succession.

Militant advocates of Kemp-Roth tax reduction, both inside the administration and on Capitol Hill, see that war as the backdrop for Baker's coolness toward deep tax reduction. They attribute the White House emphasis on spending cuts at the expense of tax cuts to Baker and his lieutenant, White House staff director David Gergen (another Bush campaign veteran).

When Baker came down hard against deep tax cuts on dividends and interest ("unearned" income) as proposed by Rep. Jack Kemp, this was viewed by many supply-siders as an attack on Kemp in Vice President Bush's behalf in the succession sweepstakes. That collides with the reality that Baker has not been all that close to Bush since joining the Reagan campaign last August. It is said around the White House that Jim Baker's man really is not George Bush but Jim Baker.

Whether Kemp contests Bush for the presidential nomination, there remains a battle for the soul of the Grand Old Party -- less liberal versus conservative than moderate versus radical or "country club" versus "right-wing populism." The litmus test for choosing sides in that war is a single issue: tax reduction, pioneered by Kemp but ridiculed as "voodoo economics" by Bush.

The listless White House campaign for tax reduction suggests that Baker and his colleagues have chosen to oppose "voodoo economics." But a somber joke passed around by supply-siders says they have a mole in the White House -- Ronald Reagan. That would add a complicating puzzle in the Republican war of succession for the canny Jim Baker to ponder.