The squat, barracks-like U-shaped building off Hsin Yi Road in bustling downtown Taipei tries hard not to look like an embassy.

Encircled by apartment houses and office buildings, it flies no flag, has no ambassador and no Marine guard.

The only thing that identifies it is a small brass plaque at the gate that says, American Institute in Taiwan, which not long ago would have sounded like a CIA cover. In fact, the building was once the base for CIA operations here. The compound also housed a U.S. military advisory group.

The Americans who work at the AIT, which is an embassy in virtually everything but name, are either "retired" or "on leave" from the State Department. Their cars carry Taiwanese, not diplomatic license plates. And, unlike diplomats, they must pay tolls on the freeways.

Whether they have diplomatic immunity is open to question pending an agreement with the Chinese Nationalists, who claim to be the sole government of all China more than 30 years after they were chased off the mainland by the Communists.

If they had a traffic accident they would hope for -- and no doubt get -- the equivalent of diplomatic treatment. Meanwhile, they carry car insurance and drive with care as becomes their "unofficial" status as Washington's nongovernmental link with Taiwan.

But being inconspicuous is something that Americans seem not conspicously good at. The AIT's carefully cultivated low-key image has become a casualty of the American election campaign, thanks to Republican presidential nominee Ronald Reagan, a longtime friend and admirer of Taiwan and its 17.5 million people.

Reagan created a major flap by saying he favored restoring "official relations" with Taiwan. Because the United States switched its diplomatic recognition from Taipei to Peking 18 months ago, that sounded like turning back the clock and brought Reagan's statemanship to question.

Now it appears that what Reagan really meant was that if he is elected he will see that Taiwan gets a better deal under existing arrangements.

"That's what we thought he meant all along," a Chinese Nationalist source said, "and we welcome it. But it was up to him to say it, not us."

While they have not forgiven the Carter administration for "abandoning" them, and as much as they would prefer to see Reagan in the White House, the Nationalists are too shrewd to inject themselves into an American presidential campaign.

The Nationalist government "does not wish to get involved in American politics" and "is not prepared to make any comment" on the so-called "China issue," Vice Foreign Minister Frederick F. Chien said recently.

That means that the Nationalists know they have a friend in Reagan if he is elected, but that they also see no need to antagonize Carter if he is reelected.

Even if Reagan wins, no knowledgeable Chinese here expects him to try to reestablish diplomatic ties with the Nationalist government. Quite apart from undoing what has been done, that would amount to a "two-China" policy -- anathema to both Taipei and Peking.

What the Nationalists would expect is more favorable treatment, including "more officiality" in their day-to-day dealings with the United States. One "more officiality" in their day-to-day dealings with the United States, One of the Nationalists' grievances is that AIT officials are forbidden to make office calls. The result is that diplomatic business must be conducted over lunch, dinner or drinks.

Reagan's public advocacy of the Chinese Nationalist cause may actually have the Nationalists more harm than good.

"If you want to help Taiwan, the best thing to do is keep quiet about it," said Charles T. Cross, the Chinaborn head of the institute, and, in effect, the ambassador. "That's what I tell everybody around here."

Steering a course between Peking and Taipei, Cross continued, "requires more, not less, diplomacy. On the one hand, we must be careful not to damage the Nationalist government's confidence in itself. And on the other we must not endanger our relationship with Peking."

Critics of Carter administration policy complain that it has gone so far to please the Chinese Communists that it has needlessly humiliated the Nationalists.

One example they cite is that the Japanese, who operate here under what they call the Interchange Association, openly visit the Nationalist Foreign Ministry and other government offices.

"The Chinese Communists couldn't care less," one American said, "but if we asked Peking if it was OK for us to do the same thing, of course they would say no."

Earlier this year, an incident occurred that reflected what many see as the absurdity of the present U.S.-Taiwan relationshp. A high-powered congressional delegation visited Taiwan in a U.S. Air Force plane, but none of the military personnel aboard was allowed to debark. The plane flew on to Okinawa, returing three days later to pick up the delegation.

The reason: Washington promised Peking that it would withdraw all military forces from Taiwan and the presence of the Air Force plane might have been construed as a violation of the agreement.

The AIT is unique in U.S. foreign relations; there is no precedent for it. It was was created by Congress under the Taiwan Relations Act. Some legal scholars doubt that it imposes American law on a foreign country.

But it was the price the United States had to pay to establish diplomatic relations with the mainland while at the same time protecting Taiwan.

Within limits set by Congress, the AIT functions pretty much like an embassy. All matters are funneled through the AIT, which has a counterpart in Washington called the Coordinating Council for North Americn Affairs, headed by a former Nationalist ambassador.

Because there are no diplomatic relations between the two capitals, the consulate has been renamed the "travel section," and what was the political section is now the "general affairs section."

Despite its shortcomings, the arrangement is working. Trade between Taiwan and the United States is 29 percent ahead of a year ago and is expected to exceed $10 billion by the end of this year.

More Taiwanese are visiting the United States than ever before. The institute's travel section processed a record of 10,025 visas in July, a 100 percent increase over the same month of 1978, when there was still diplomatic relations.

To keep up appearances, all visa applications are telexed to the U.S. Consulate in Hong Kong for approval. Thus the visa stamped in a Nationalist Chinese passport here is "issued" in Hong Kong.

After a year's moratorium on arms sales to Taiwan during 1979, the United States in 1980 has sold the Nationalists government more than $800 million worth of military hardware.

But the Nationalists are not satisfied. They want more sophisticated missiles and a new-generation fighter, preferably the front-line F16, to replace their F5Es, which they say are out of date even though they are superior to China's ancient Migs.