Ronald Ray Howard was caught in Victoria, not far from the shooting scene along U.S. Highway 59 near Edna. He wrecked the SUV, which he had stolen, by crashing it into a house, then tried to flee on foot.
When Davidson, 43, died three days later after never regaining consciousness from the 9 mm bullet wound to the neck, Howard was charged with capital murder.
Howard was set to die Thursday evening.
The lethal injection would make Howard the 14th convicted killer executed this year in the nation's most active capital punishment state.
Attorneys were in the federal courts trying to block the punishment.
The music blaring from the radio made the slaying more notorious. At Howard's trial, his lawyers blamed hours and hours of incessant gangsta rap music - with lyrics advocating the death of police officers - as contributing to his actions. The defense sparked a national debate on the violence-laden anti-police music and censorship..
"He grew up in the ghetto and disliked police and these were his heroes, these rappers ... telling him if you're pulled over, just blast away," his trial attorney, Allen Tanner, recalled last week. "It affected him. That was a totally valid serious defense. It really was."
"I'm not a psychologist," Howard said Wednesday. "So I don't know. I never said: Yes it did or no it didn't. I don't know. But my lawyers thought it could have caused it. And they were trying to justify, put reason, for what I did."
But Howard said the shooting was also the result of being pulled over by police "plenty of times" in his hometown of Houston and never having good experiences with officers.
At the time of the April 1992 shooting, the 18-year-old father of four was on probation for stealing a motor vehicle. He acknowledged Wednesday that he stole "a lot of cars" but said it was the normal activity for kids in his Houston neighborhood.
Jurors in Austin, where Howard's trial was moved because of publicity in Jackson County, convicted the seventh-grade dropout after 40 minutes of deliberations. The same panel deliberated six days before deciding Howard should die.
Howard told a grand jury he was listening to "Soulja's Story" by Tupac Shakur before he shot Davidson. The song makes references to a young black male being pulled over by police, remembering Rodney King whose videotaped beating by Los Angeles police led to deadly riots in 1992, then opening fire on an officer. Shakur was gunned down in 1996 in Las Vegas, a slaying that remains unsolved.
Testimony showed Howard was a drug dealer and gang member. Prosecutors argued the rap music defense was a diversion intended to mitigate Howard's viciousness, the AP reports.