The ATF said the bombs appear to have been made by the same person or people because their design was identical.
An explosive was placed inside the flashlights with a smaller battery and rigged so that turning it on would send an electrical current that triggered the blast, Mangan said.
The first bomb was spotted by a passerby on May 13 in a suburb just west of Phoenix. It was sitting behind a palm tree in a strip mall and blew up when it was clicked on.
The next day, about 10 miles away, a landscaper found a flashlight in an irrigation ditch. It, too, exploded when he flicked the switch, authorities said.
The third bomb exploded on May 24 at a Salvation Army distribution center near downtown Phoenix.
An employee detonated the device while sorting through donations, forcing 120 people in the store to evacuate. Jon Bierd, production manager at the facility, said the worker suffered a small abrasion to his forehead.
The Salvation Army stopped accepting donations of flashlights. Since the explosion, employees have not seen any flashlights matching the yellow one seen on the billboards.
"If we have a flashlight that's heavy or is not empty, then I'd call the Phoenix Police Department. No matter where it is, we do not touch it," said Bierd, who is setting aside any donated flashlight.
In addition to the billboards, police are offering a $10,000 reward for tips.
Police have received dozens of calls reporting possible flashlight bombs that either turned out to be false alarms or hoaxes, including one from a Goodwill store.
Meanwhile, the bombings have stopped, though it is unclear whether there are more flashlights out there.
The attention may have scared them off or they may gain confidence and strike again as the investigation stretches on without an arrest, criminal profiler Gregg McCrary said.
Details of the case lead the former FBI agent to think the culprit is either a man or two men, with one of them being a dominant leader and the other a follower.
As for motive, whoever is responsible may be bombing at random for various reasons, said McCrary, who teaches at Marymount University in Virginia.
"Typically these things are about wanting to feel superior and smarter than other people," he said, adding that the bomber also might revel in the news coverage.