Eugene is the principal of the Motabeng Secondary School in the village of Motabeng, the place of which Elizabeth says, "I going to live here some day" before climbing the school yard fence to go and fetch her son. It is Eugene who tells her that her son is not there, but out playing, while his wife makes tea for Elizabeth.
Eugene is a secondary character whose name shows up only periodically throughout the novel but who has great influence over Elizabeth. Yet, like many secondary characters, he helps develop Elizabeth's character by bringing out character traits that relate to the progress and conflict of the plot, for instance, when he says to her "You don't seem to get along with the local people." This allows Elizabeth to explain that she is an outsider, used to isolation, and that because she is an outsider, people don't care if they get along with her, especially the locals of Batswana:
"You don't seem to get along with the local people," [Eugene] observed.
"It's not that," Elizabeth said, anxiously. "People don't care here whether foreigners get along with them or not. They are deeply absorbed in each other. ... I don't care whether people like me of not. I am used to isolation."
Another way in which Eugene helps develop the plot is by bringing out the premises that drive the plot through the conflicts toward the climax. Eugene is from South Africa. He is in Batswana to educate "the black man" and their children. The educational and school brochures he writes makes the blacks of Batswana feel like an education will allow every family to have tables brimming with good food and every family member to be clothed. The narrator then contrasts this with South Africa where they had never felt this same way. They had their belief that "the black man" was incapable of higher thought needed for education and incapable of higher living. Eugene, having a connection to both places and to both beliefs, allows these contrasting concepts to be explicitly developed by the narrator, which in turn allows the plot premises to be developed.
The pamphlets [felt like] good food; roast chicken, roast potatoes, boiled carrots, rice and puddings. ... like food and clothes and opportunities for everyone. It wasn't like that in South Africa. There they said the black man was naturally dull, stupid, inferior, but they made sure to deprive him of ... education...
Another way Eugene helps advance the plot is through his characterization as sympathizer with African people and the African continent. For example, when the agricultural training and Peace Corp programs are being explained by the third-person narrator, it is explained that Eugene has "humanity" that others lacked because it was only he who "blurred the dividing lines between the elite ... and the illiterate" since he provided programs that gave benefit to both elite and illiterate, like the agricultural training program he initiated. This unity Eugene sees is attributed to how deeply he sympathizes with "the black man." In a flashback to her afternoon in Eugene's house, Elizabeth wonders at how his "humble manner" can be so nearly "identical" to African laborers' own "gestures and postures." This sympathy affects the plot development by revealing motivation and bias behind conflicts.
'How is it his movements and gestures are so African? ... [I]t's an unconscious humility.'
Another couple of places to look at for how Eugene advances the plot might be (1) when Elizabeth takes her son in a taxi back to Eugene because he had said "'I'll help you,'" and (2) when Elizabeth is ill.