You zombie geek should be an elitist, always on about how much smarter he is than the rest of the students. He should only eat the brains of the most intelligent of students, as to do otherwise would dilute his already massive intellect; fortunately for the story, this means he doesn't eat any of the other characters' brains, for they are all far below his standards.
Perhaps as a part of the punchline, he should eat the brains of whoever it is that comes up with the brilliant solution to whatever problem ends up driving the plot - and everybody takes it as a compliment and laughs?
Student1: "Wow Jimmy, you saved the day!'
Student2: "Good thinking Jimmy!"
Student3: "Jimmy, you're a genius!"
ZombieG: "Hey Jimmy... you know what this means..." *GLOMP*
Students: [uneasy pause] . . . *laughter*
FIN