A serial sex offender has been found guilty of killing four women — crimes that were mostly committed while he was being tracked by GPS and that now make him eligible for a death sentence.

Victims’ relatives clutched hands in the Orange County courtroom and closed their eyes while the guilty verdicts against Steven Dean Gordon were read. Some trembled and some cried.

“I can’t say it’s justice but it’s peace. It’s a little bit of peace,” Jodi Estepp, the mother of 21-year-old victim Jarrae Estepp, told Associated Press outside the courtroom.

Gordon, who partly blamed his actions on probation officers for failing to keep track of his movements, showed no emotion in court. He also told police he had killed a fifth, unidentified woman.

Jurors also found Gordon guilty of special circumstances of murder during a kidnapping and multiple murders, which will make him eligible for a death sentence.

A penalty phase will begin on Monday when jurors will decide whether to recommend a death sentence or life in prison without parole.

Authorities said Gordon, 47, and 30-year-old sex offender Franc Cano, who is being tried separately, abducted and killed four women. Prosecutors charged both men with rape but later dropped the rape charges against Gordon without explanation.

Investigators said they pieced together the case after Estepp’s body was found on a conveyor belt at a recycling center in Anaheim in March 2014.

Yolanda Linder, left, and Jodi Estepp, aunt and mother of Jarrae Estepp, one of four murder victims of Steven Gordon outside Orange county court on Thursday. Photograph: Sam Gangwer/AP

Authorities said the men’s tracking devices linked them to the disappearance of the other three women in Santa Ana in October 2013 — Kianna Jackson, 20, Josephine Monique Vargas, 34 and Martha Anaya, 28. Their bodies have never been found. All four women had links to prostitution.

Jodi Estepp said that she felt her daughter’s death was not in vain because her body led to the men’s capture.

“I just wish they would have let her go,” she said. “It’s difficult to say, very difficult to say ... but their killing her got closure for those other families – and they can’t kill again.”

Gordon, who represented himself at the trial, confessed to authorities in an interview played for jurors about his role in the killings.

Gordon and Cano were registered sex offenders after being convicted in separate cases of lewd and lascivious acts with a child under 14. Gordon was convicted in 1992 and also had a 2002 kidnapping conviction, while Cano’s conviction dates back to 2008.

At the time of the killings – which took place between October 2013 and March 2014 – Gordon was living in an RV in an industrial area of Anaheim where the men brought their victims. He wore a GPS device during at least three of the murders, according to grand jury testimony.

In addition to Estepp’s murder, the authorities charged the men with killing three women Police believe Cano and Gordon had known each other since at least 2010, when Cano cut off his GPS device and fled to Alabama, where he was arrested with Gordon. Two years later, they again cut off their monitoring devices and boarded a Greyhound bus to Las Vegas using fake names before being arrested two weeks later by federal agents.

Cano has pleaded not guilty. His next court appearance was set for 29 December.