We must infer the causes for which the American hesitates at the other tracks while he has another drink at the bar; he might possibly be thinking about how he might bring the relationship to an end. What are Jig’s wishes?

It is not at all clear from this story what Jig's wishes actually are at any point. Indeed, the only time she explicitly asks the American to do anything is when she asks him to "Please please please stop talking." She does not want to hear him ask any more whether she truly wants to do what he wants. This makes it difficult for either the reader or the American himself to interpret what it is that Jig truly wants to do.
She is an indecisive character, and it appears from her behavior that she feels somehow beholden to the American. Possibly she loves him; possibly, she is afraid of him; possibly, both are true. At any rate, she wants to do whatever will make him happy. It is impossible to glean from the story what Jig truly wants to do with her life.