I have to be prosecutor for a semi-mock trial, and I was wondering how you would win the case. Chapters 17-19 will probably be helpful in answering this question. I have to prove that Tom is guilty, and pretty much disprove everything Atticus brings up. This is hard since it's pretty obvious Tom is innocent but please try your best.
Yours is a tough position because, although you win, you are not in the right. Tom Robinson is not guilty, and you have to know that. Your only choice, short of going on the attack against this humble black man, is to prop up the testimony and actions of Bob and Mayella Ewell. The jury is already on your side, so do what you must to ensure their outrage at a black man who stepped into a room alone with a white woman and stayed there. It is shameful but necessary for this project.
He knows he can rely on the prejudices of the jury. As long as Tom is black and Mayella is white, that's all he needs. Even if they believe that he didn't rape her, they still think he had a relationship with her. In those days in Maycomb, that would have been enough to convict him. The fact that he said he felt sorry for her was the nail in his coffin.
I think that the point your teacher is probably trying to make is that a fair trial would not have found Tom guilty. So you're in a tough position.
I think that you have to try to play it like a prosecutor would back then. You have to play on racial fears. You have to ask why Tom keeps hanging around Mayella and imply that he wants her sexually. You have to try to bring out the idea that a white woman would never want to get involved with a black man.
You don't have to be overtly racist. You can ask Mayella "as a white person in Maycomb, how do you feel about black people?" "Do you think they are equal to you?" "Would you ever ask a man to kiss you?" Things like that that would make it clear that Mayella would not have asked Tom to kiss her the way he says she did.
Since this trial has taken place in the 1930s, evidence from DNA is unavailable, so there is no scientific method of determining that Tom Robinson has committed rape or the other actions of which he has been accused. By his own admission, he has entered the Ewell shack, so what has happened inside depends upon the testimony of Tom and the Ewells. In order to refute this "evidence," Atticus Finch foils Tom Ewell's attempt to implicate Tom for the beating which he has issued Mayella by the evidence that the marks of Mayella have been made by a left hand and arm, while Bob Ewell is left-handed and Tom has no use in his left arm.
So, to refute the logic of Atticus is virtually impossible for Mr. Gilmer unless Bob Ewell was injured prior to the incident under question and did not have use of his left arm. It seems that the only thing left for Mr. Gilmer is to try to find a "witness." Perhaps he can find a person or persons who have overheard Tom talking outside church or a store about Mayella. If this witness only heard only snatches of his conversation, the witness may testify that Tom mentioned how Mayella deserved attention or something that could implicate him since his words suggest an interest in her. Someone, also, may have heard Ruth and Tom arguing and Tom's having told her something to the effect that he doesn't have to have her for love because someone else will love him.
Actually, Gilmer does win the trial, so I would go about it similarly to how he did. First, a prosecutor needs evidence and witnesses. I would ask questions of Heck Tate in order to get the information that Bob came running that his daughter had been raped/attacked. Then I would get Bob to show on the stand how he was a witness to it all. Along with that, I would use the evidence that the room was disturbed by a chair that was knocked over, and his daughter was beaten pretty badly.
Another angle that would help Gilmer is motive. Tom stopped by several times over the seasons to help her. He never once received any money for his work, so that could be motive. Gilmer could show that Tom was frustrated that he didn't get anything in return. And the fact that he was so big and strong could counter the fact that his left arm was useless. He was strong enough to hold her down with one good arm.
I think it would get too ugly if you tried to use the racial approach in a mock-trial. The fact that Tom "felt sorry" for Mayella and almost called her a liar in chapter 19 was enough in that time period to convict him, too. It is an approach that would work in that setting though (sadly).