TOKYO -- As Japan's first new government in six years takes office amid international financial crisis, the unhappy U.S.-Japanese relationship faces a test: Shall the voluntary agreement limiting auto exports to the United States be renewed for a sixth year?

Although that decision is six months away, it is in the thoughts of government and industry policy makers here. Many acknowledge the auto quota serves no useful purpose but is a hypocritical gimmick papering over but actually reinforcing current U.S.-Japanese sickness.

During 18 years of reporting visits here, we never before saw relations between the world's two economic superpowers as threatened by emotional animosity. Just as bold steps are needed to cope with global economic challenges, the sometimes daring Prime Minister Yasuhiro Nakasone gives way Nov. 6 to a more conventional Japanese politician, Noburo Takeshita.

Reknowned as a deal-maker, Takeshita would be in character renewing the voluntary auto quota. Actually, it was not so ''voluntary'' when first imposed by the new Reagan administration. Whether or not the quota helped revive Ford and Chrysler, it surely has cost the American auto buyer.

What's more, all concerned here view the agreement as counterproductive in a soft American car market when, because of the higher yen, only Toyota and Honda are fulfilling quotas. The other companies -- worried about ''prestige,'' according to one Japanese auto executive -- furiously seek to avoid falling short of their quotas. Thus, ending the agreement likely would reduce, not increase, exports to the United States. Instead, published reports suggest a 10 percent reduction in the quota to make ''prestige'' more easily maintainable. Ministry of International Trade and Industry officials told us this report is wholly false, but it looks like a trial balloon that failed.

Since the Reagan administration three years ago was ready to end the quota, why do the Japanese stick with it? Because, they say, it is still supported by Detroit's Big Three and the United Auto Workers -- and therefore Congress. ''Yes, we would like to end it,'' a senior Japanese official told us. ''But if we did, would the administration protect us from Congress?''

But inside the Japanese auto industry, sinister motives are perceived. ''We are victims of the politicians and MITI,'' one executive told us. He sees the auto quota covering up the last two great redoubts of Japanese protectionism: agriculture and construction. Ominously, these special interests are key supporters of Takeshita.

Keeping out American farm products and contractors is hidden by attention to autos. Supposed no-tariff restrictions on cars do not slow the increasing flow of German BMWs and Mercedes. Japanese industry and government agree that no American cars are sold because Detroit does not try.

Hypocrisy is mutual. Instead of letting in farm products and construction firms, Japan negotiated a cartel with the United States regulating semiconductor prices. Its alleged violation, however, triggered U.S. retaliation and more bitterness here. Senior Japanese officials fear President Reagan will sign a potectionist trade bill. They complain the United States even now acts as prosecutor, judge and jury in antidumping cases.

Bitterness is not limited to the power elite. Members of Congress smashing Toshiba equipment (after the company's illegal sales to the Soviet Union) was a one-time event in the United States, but was shown repeatedly over television here and was cited to us by a wide range of angry Japanese.

One farsighted escape hatch from petty bickering is Ambassador Mike Mansfield's proposal that Japan and the United States negotiate a free-trade agreement similar to the U.S.-Canadian pact. When he first suggested it last year, Mansfield elicited no interest in Washington. Japanese officials dismiss it as visionary.

Yet, we found widespread informal interest here, including some from surprising sources such as MITI Vice Minister Makoto Kuroda, the notorious hard-line negotiator. If free trade requires too much courage at the highest level in both governments, junking the auto quota and rejecting its hypocrisy at least would be a small first step.