Evan Squires, 70, and his wife Wilda Squires, 65, of Minnedosa, Man., were snowbirds who regularly spent the winter months in Weslaco, Texas.
The seniors were shot and killed in their mobile home in the Magic Valley Trailer Park on Nov. 13, 1988.
In 2011, police made an arrest after allegedly matching a DNA sample to feces found at the crime scene.
Arturo Almaguer, 44, has pleaded not guilty to capital murder charges.
Assistant district attorney Joaquin Zamora said he expects the case to go to the jury in the next few days.
Jurors heard from all of the prosecution's nine witnesses on Tuesday, the first day of the trial, before they went on a break for two days, said Zamora. He couldn't say whether the defence plans to call any evidence, but closing arguments are to be made Friday.
Defence lawyer Pamela Alexandra refused to comment while the case is ongoing.
Zamora said it was hard to put the case together since many witnesses, some seniors who also lived in the trailer park, have died. "It was very difficult even to find some of the officers that were involved because some have either passed on or they're nowhere to be found."
Evan Squires was shot once and his wife twice, said Zamora. It appears the two had been sleeping before the shooting because they were wearing pyjamas.
Police who later examined the trailer made an odd discovery: feces on the floor, underneath someone's blue-jean shorts.
Zamora said officers tracked down known drug users and thieves in the area and came up with various suspects.
"Nothing actually ever panned out," he said. "(The case) dried up after that first year."
But experts were able to collect enough skin and blood cells from the feces to get a DNA profile. Authorities said they got a match when Almaguer was arrested on an unrelated offence in Michigan.
Zamora said his office has elected not to seek the death penalty if Almaguer is convicted.