Ed Traxler was a hard-working, pragmatic, honest cop and a lieutenant in the Central Division of the Police Department in 1984 and was one of the investigators assigned to the Phone Book Killer case. He also seemed to have a thing for cigarettes and coffee (even if the coffee was cold). He didn't like listening to Hal's stories. He also seemed ready to consider Reese's story.
As of 1984, Ed Traxler was a hard-working, pragmatic, honest cop about seven years from retirement (though it's unknown if this was a regular or early retirement). He was a seasoned lieutenant of the Los Angeles Police Department and worked as a homicide detective alongside Hal Vukovich, with whom he was on a first-name basis, although he didn't seem to like listening to Hal's stories. He also seemed to have worked with Dr. Peter Silberman sometimes. He could be most often seen with a coffee and a cigarette with him, even if the coffee was cold.
Ed was at the police station drinking coffee and casually ignoring a criminal who was refusing to be put in a cell. His partner Hal Vukovich gave him a file on two Sarah Connors that had been killed. Traxler failed to see the connection at first until Hal showed him their names. Traxler said that this was a "one-day pattern" killer.
At about 9:40 pm that night, the phone book killer case drew many news paper interviewer's to the station which Hal said, "Oh shit". The interviewers tried to get answers, but Traxler turned them down, much to their annoyance. Ed asked Hal if he had reached the next girl yet, but Hal said he just got her answering machine. Ed told him to send a unit but there was no answer but Hal did have the unit remain outside the house. Traxler had Hal call her again while asking for a smoke, not noticing that he was holding one already, but it was revealed on the other end that Ginger Ventura and Matt Buchanan in Sarah's house were having sex and did not answer it.
Sarah wasn't even there as she went own after being turned down on a date. Ed decided to give a statement to the interviewers who were still outside his office to get Sarah to call them and get a hold of her. He asked Hal if he looked appropriate for the camera. Hal said he looked like shit. Ed said, "Your mama." Ed later got the call he was expecting from Sarah Connor from the bar Tech Noir. She told him that someone might be following her. He told her to stay visible till a car got there.
Ed and Hal found out that Sarah had been abducted by Kyle Reese (whom they believed to be the killer at first) and headed out in a car to find him. After arriving at the apartment, Traxler noticed Sarah in a car with Reese and told a nearby police car to follow him and prepared to follow themselves.
Ed later discovered Ginger and Matt's bodies at the apartment who had been killed by the T-800. The police found Sarah and brought her and Reese to the station. Sarah was told of Ginger and Matt's deaths and burst into tears. Traxler comforted her as she cried. Traxler even gave her his coffee. Traxler told Sarah to tell Dr. Peter Silberman everything Reese told her. Silberman interviewed Kyle Reese and Kyle told Silberman the truth: he was a soldier from the future sent by John Connor to protect Sarah. While his colleagues Hal and especially Peter Silberman simply assumed Kyle Reese was crazy or on drugs, Ed was more sympathetic to him and Sarah Connor and appeared to be at least somewhat persuaded by his argument.
After seeing Silberman question Resse, Traxler and Hal stepped out for a break. Ed contemplated the interrogation in his head. Hal suspected that Traxler believed Reese and tried to talk sense into him. Hal said "Come on Ed, that was moon talk. The guy's a wacko". When Traxler responded with, "He better be.", Hal began to realise after this conversation, that even he could not rule out he may have told the truth.
After Silberman interrogated Reese, Ed, Hal, Sarah, Silberman and an unknown police officer watched the interrogation on a television. Ed still seemed to believe the statement Reese made while everyone else was still unconvinced. Ed told Silberman to stop the recording when Reese started talking about the Terminator killing Sarah by ripping out her heart. Hal gave Ed a bullet proof vest. Ed showed it to Sarah and her told her that the murderer must have been wearing one to avoid being killed by Reese's gunshots. Ed told Sarah to sleep on the couch until her mother arrived. Ed told her to sleep on the couch and not worry as 30 cops were on guard in the building.
When the T-800 raided the police station, Ed was one of the officers to fight against it. He locked Sarah in a room to stop the T-800 from getting to her and hid with a rifle in a room down the hall waiting for the T-800. He open fired on the Terminator but the infiltrator returned fire and shot Ed multiple times in the chest and severely wounded him. Ed, wounded, laid next to a draw when Hal found him and open fired on the Terminator in rage but was fatally shot.
Ed, wounded, was later shown handing his sidearm to Kyle, telling him, "Reese! She’s got to stay alive. Do whatever you have to do.” From this scene, it is obvious that Ed Traxler believed at least part of the story that Reese told in his interview with Dr. Peter Silberman, or became a believer when his gun did little damage to the T-800.
Traxler presumably died from the injuries he received.
Behind the Scenes
- Traxler featured in a number of short scenes — which seemed to confirm his belief in Reese's story — that were cut from the film primarily to speed up the advancement of the plot.
- In the original script, Traxler's rank (and dialogue) were reversed with that of Hal Vukovich.
- Traxler seemed somewhat persuade by Reese's story as shown in a deleted scene.
- Although there is little evidence to support his death, the official script does read as follows: "They find the Lieutenant propped in a corner, dying." 
- Agent Auldridge in Terminator: The Sarah Connor Chronicles series finale "Born to Run" seemed similar to Traxler in many ways and appeared to partially believe her story.
- His belief of Reese's story is highly discussed among fans.