ALTERNATELY hostile and accommodating in the past few weeks, Jesse Jackson has caused little trouble for his party. While he feigned tough stands on certain issues--namely South Africa--he promised to keep floor fights to a minimum. And while he expressed anger over not being consulted about the selection of the convention's keynote speaker, Jackson's appointment of well-respected politico Ron Brown to handle his convention strategy was widely seen as a gesture of good will towards the party.

But while the party's mainstream is letting out an almost audible sigh of relief over Jackson's post-defeat behavior, for his part, Jackson seems to be making the least of his loss.

His showing in the primaries and caucuses were by all accounts historic, and in real terms, impressive. Jackson fared better than Dukakis on Super Tuesday, winning a host of Southern states including Virginia. He won caucuses in states with small Black populations, such as Alaska and then, stunningly, Michigan--trouncing the Massachusetts governor by a nearly two-to-one margin there.

For a brief time, the possibility of Jackson appearing on the ticket became a probability, and it even seemed possible that Jackson might enter the convention with the most delegates. As it is, he comes in with over 1000.

The results of his campaign were sufficient to lead Hendrik Hertzberg to exclaim that Jackson has proved himself to be the most important Black leader in the country's history next to Martin Luther King, Jr. and Booker T. Washington.

BUT as each week passes, Jackson's influence seems to diminish. Both The Boston Herald and the Globe ran page one headlines telling of the way Dukakis' forces successfully trounced the Jackson delegates as the party's platform was drawn up.

With a huge and loyal constituency, Jackson should be able to wield influence in this fall's election. But it seems ever more likely that the Jackson campaign of 1988 will go the way of the Jackson campaign of 1984--ceasing to matter after the convention. Unless he chooses to make a dramatic turn either in favor of or antagonistic to the party's all-but-certain nominee, Michael S. Dukakis, Jackson will be of no more significance in the fall election than the other five dwarves who failed to capture the nomination.

In 1984, through the skillful negotiating tactics of Mondale's point man on the issue, Robert Beckel, the Jackson factor was effectively neutralized. The result was that Mondale got little in the way of fervent support from Jackson and his followers, but more importantly in the eyes of the Mondale campaign, he got little in the way of outright opposition. Talk of forming a third party ended up being just that.

That pattern seems likely to repeat itself, so long as Jackson continues to follow the uncertain course he's on now. At first it seemed that he would accept his loss and merely try to contribute to the debate within the party. Then he switched, suddenly seeming to set his sights on being nominated to the vice presidency. Saying that he had no ranch, no ski-lodge, no oil company to run, Jackson let it be known that the vice presidency was hardly something he would categorically dismiss.

But Jackson won't out right say that he wants to be vice president; he won't even say that should be asked to be vice president. All he says is that he should be seriously considered. And it now seems that he has been considered. No one, probably not even Jackson himself, thinks that he will actually be offered the job.

JACKSON could choose to be a true thorn in Dukakis' side. He could issue ultimatums behind which his constituency could rally. He could lay out a sensible case for his being placed on the ticket--one that goes beyond his supporters' current contention, that since he came in second he has earned the spot, as if history backed up such an argument. He could defiantly challenge the party to open up, to acknowledge itself as the party of the left, just as the Republicans admitted they were the party of the right by nominating Reagan in 1980.

By employing what he modestly calls Jackson action, Jackson could make himself a force in the fall election. If the Democrats failed to live up to his demands, he could take his followers on a run from the party--making the Democrats realize once and for all that Blacks no longer are Democrats first.

Or he could do the more gracious thing, and perhaps in the end the more politically astute thing, going all out in support of Dukakis, mobilizing the hundreds of thousands of new voters he claims to have brought into the party. Jackson has long maintained that he is an important phenomenon in American politics because he has given people long locked out renewed--and in some cases, just plain new-faith in the system.

But he has yet to demonstrate that this faith extends beyond his own fortunes. Are those willing to go to the polls to pull the lever for Jesse also willing to pull the lever for the Duke if Jesse gives them the go ahead? In 1984, the Jackson camp claims, the signal was never given because the nominee didn't deserve the support. But could it be that the real reason is that Jackson fears that he may fail to deliver the votes he says he has brought to the party?

So far, Jackson has carefully refrained from putting himself on the line. He has proven that among Democratic candidates, virtually all Black voters prefer him. As it stands now, he regularly can be counted on to attract virtually all of the Black vote in the Democratic primaries, and to garner about 30 percent, at the most, of the total popular vote during the quest for the nomination.

Nothing shows yet that he can go beyond that figure, and until he proves that he will do something with the 30 percent support he seems to have a lock on, the party will have precious little incentive to answer to him.