Nashville Police Chief Steve Anderson said there was no clear motive, though Reinking may have "mental issues." He may still be armed, Anderson told a mid-afternoon news conference, because he was known to have owned a handgun that authorities have not recovered.
"He's on foot," Anderson said. "Unless he's been picked up by a car, he would be fairly close. We don't want to alarm people, but certainly, everybody should take precautions. It could be he's in an unoccupied house. We want everybody to be concerned. Neighbors should check on each other."
Officials with the Nashville public school system say schools will go into "lock-out" mode if Reinking isn't found in time for class Monday. During the lock-out students will be free to move about the building but no guests or visitors will be allowed to enter the building.
The search continued as police reports from Illinois came in that portrayed Reinking as a disturbed man with paranoid delusions, and one who liked firearms.
The reports were among multiple past red flags about the suspect, who had just recently moved to Nashville from Morton, Illinois.
Reinking was arrested by agents with the U.S. Secret Service back in July after he crossed a restricted area near the White House, officials said. He was detained after refusing to leave, saying he wanted to meet President Donald Trump.
In May 2016, deputies from Tazewell County, Illinois, were called to a CVS parking lot. Reinking told officers that Taylor Swift was stalking him and hacking his phone, and that his family was also involved, according to a report released Sunday.
It is not clear why Reinking moved to Nashville and if it had anything to do with being near the pop/country superstar. Police say he was employed in construction for a while and there would have been enough work in the booming city for him.
In August, after the White House incident, Reinking told police in Tazewell County, Illinois, that he wanted to file a report about 20 to 30 people tapping into his computer and phone. He also complained that people were "barking like dogs" outside his residence, according to a report.
Reinking agreed to go to a local hospital for an evaluation after repeatedly resisting the request, the report said.
Another report from the sheriff's office said Reinking barged into a community pool in Tremont, Illinois, last June and jumped into the water wearing a pink woman's coat over his underwear. Investigators believed he had an AR-15 rifle in his car trunk, but it was never displayed. No charges were filed.
Reinking was not armed when he was detained near the White House. However, state police in Illinois, revoked his state firearms card at the request of the FBI and four guns were taken from him, authorities said. The AR-15 used in the shootings was among the firearms seized after U.S. Secret Service agents arrested him last July.
Sheriff Robert Huston in Tazewell County, Illinois, said deputies allowed Reinking's father to take possession of the guns on the promise that he would "keep the weapons secure and out of the possession of Travis." Huston added that, based on deputies' encounters with Reinking, "there's certainly evidence that there's some sort of mental health issues involved."
While Huston said it was unclear how Reinking reclaimed the guns, Nashville Police spokesman Don Aaron said that his father "has now acknowledged giving them back."
Phone calls to a number listed for the father, Jeffrey Reinking, went unanswered.
Police recovered three of the four guns that were originally taken from Reinking, officials said. They believe he is armed with at least one handgun.
Reinking, police said, drove into the Waffle House parking lot in his gold Chevy Silverado pickup and sat there for about four minutes before opening fire outside the restaurant.
The victims fatally shot in the parking have been identified as Taurean Sanderlin, 29, of Goodlettsville, and Joe Perez, 20, of Nashville.
Sanderlin was an employee at the restaurant.
Perez's mother posted a picture of her son on Facebook and asked for prayers, saying it was the hardest day of her life. "Me, my husband and sons are broken right now with this loss," Trisha Perez said in the post. "Our lives are shattered."
Reinking then went inside the restaurant and opened fire, police said.
One of the fatally wounded inside was DeEbony Groves, a 21-year student at Nashville's Belmont University.
Groves was remembered as an exceptional student who made the Dean's list and a tenacious basketball player.
"She was a brilliant young lady, very, very intelligent and a very hard worker," Gallatin High School basketball coach Kim Kendrick told The Tennessean.
Akilah Dasilva was also killed inside the restaurant. The 23-year-old from Antioch was a rap artist and music video producer who had such skills behind the camera that he was a favorite among many of Music City's independent musicians and recording labels, The Tennessean reported.
"Music is my life and I will never stop until I achieve my dreams," Dasilva said on his Twitter account.
Dasilva's mother told CBS News that her son was a student at Middle Tennessee State University and aspired to be a music engineer.
He was at the restaurant with his girlfriend, 21-year-old Tia Waggoner, the paper reported. Waggoner was wounded and is being treated at Vanderbilt University Medical Center.
Dasilva's family said she underwent surgery and doctors were trying to save her leg.
Police say Sharita Henderson, 24, of Antioch, was wounded and is being treated at VUMC.
Also wounded was James Shaw Jr., a 29-year-old restaurant patron, whom police said suffered minor wounds from wrestling the gun away Reinking.
Shaw, who is a Nashville native who works as a wireless technician for AT&T, said he was no hero — despite being hailed as one by Nashville Mayor David Briley.
Shaw said he saw pounced on the suspect after making up his mind that "he was going to have to work to kill me."