Why do you think Ben reappeared at the moment of Willy's final decision?
In Arthur Miller's Death of a Salesman, Willy Loman is a 60-year-old salesman whose many years on the road have apparently contributed to the mental challenges that he manifests in the course of the play.
In a number of instances, Willy imagines past events or has conversations with people from his past. One of these people is his older brother, Ben. Willy admires and brags about Ben's adventures and great achievements, and such achievements lead Willy to think that he himself can achieve great things.
Just before Willy finally does manage to kill himself, Ben, according to the stage directions, "appears in the light just outside the kitchen." Perhaps Ben appears because he represents the sort of life that Willy has dreamed of having. Just before Ben appears, Willy has had an emotional moment with his son, Biff, whom Willy declares is "going to be magnificent." Thus, I would suggest that Ben's appearance reminds Willy of the possibilities that exist for adventure and achievement. Perhaps Willy realizes that he himself cannot experience those dreams, but that his son is still young enough to have those sorts of adventures. Thus, Ben reminds Willy of the potential for a different life and Willy may kill himself in the hopes that the insurance money will provide Biff with the sort of financial foundation that he would need to undertake such an adventure.
Near the end of Act 2 of Death of a Salesman as the tormented father and son embrace eachother, Willy, astonished, remarks to Linda and Happy about Biff: "Isn't that - isn't that remarkable? Biff - he likes me! And two lines later: "That boy -- that boy is going to be magnificent! At this point, the stage directions state that "Ben appears in the light just outside the kitchen." Willy's fate is sealed. Although, Biff, now painfully self-aware, has just begged his father to destroy "that phony dream", Willy's words clearly indicate that the truth cannot pierce the armour of his self-delusion. This scene appears to justify the claims of some critics that Death of a Salesman cannot be considered an authentic tragedy since the hero never achieves the profound insight of a tragic hero. But in a kind of counter-argument to this criticism Miller provides the character of Ben, a character who takes shape at critical moments in the play as a kind of motif of Willy's developing self-consciousness. Here, at his third and final appearance, Ben's presense functions as Willy's psychological raison d'etre for suicide, thus fulfilling what tragedy obliges of its hero - death for an ideal.