Will George Zimmerman's past come to haunt him?

(CNN) -- Judge Debra Nelson heard arguments Tuesday morning on whether the jury in the George Zimmerman trial should hear about other incidents when Zimmerman reported suspicious people in his neighborhood, the Retreat at Twin Lakes.

The former neighborhood watch captain is charged with second-degree murder for shooting 17-year-old Trayvon Martin on February 26, 2012. He told police he was watching the teenager because there had been a rash of crime in the area. A conflict ensued and, he said, he was forced to shoot Martin in self-defense.

Prosecutor Rich Mantei said Zimmerman's prior phone calls reporting suspicious people in the neighborhood are relevant to the case because they help prove motive by showing his "building level of frustration."

Zimmerman's defense attorneys disagreed. "They are going to be asking this jury to make a quantum leap from good responsible citizen behavior to seething anger," Mark O'Mara said Tuesday morning.

Prosecutors called multiple witnesses in quick succession, including Wendy Dorival, who was a volunteer program manager for the Sanford, Florida, police department in 2012. She coordinated neighborhood watch programs.

Dorival said she worked closely with Zimmerman because he helped organize the program for his neighborhood. She told him a neighborhood watch volunteer should act as the "eyes and ears" of the police -- but not as a vigilante.

"If you see a car driving around in circles, and you don't recognize the car in your community, that might be suspicious." Dorival said. "If people are walking around in areas that are not typically walked on, that could be suspicious."

Prosecutors also called Donald O'Brien, president of the Retreat at Twin Lakes Homeowners Association.

"Everybody was supposed to watch out for their neighbors," O'Brien said. "If they see something suspicious, stay away and call the police."

Court ended abruptly Monday, after the trial started with opening statements, when the prosecution introduced a non-emergency call made by Zimmerman in August of 2011. He's heard reporting a suspicious person in the neighborhood and telling the operator that the neighborhood had some break-ins recently.

Prosecutors said the call helps show Zimmerman's state of mind the night Martin was killed, but the defense questioned the call's relevance.

Nelson asked attorneys on both sides to research the issue overnight and be prepared to argue their positions Tuesday morning.