Gene Hackman, Wife Betsy, Timeline of How Authorities Discovered Their Bodies

Gene Hackman’s New Mexico home is so huge, it took a while to find his body after his wife Betsy’s was found, a local fire official tells TMZ ... giving us a detailed rundown of what went down when they arrived on the scene.

Santa Fe Fire Chief Brian Moya tells TMZ paramedics responded to a "man down" call from Gene's address Wednesday with a fire engine and an ambulance, and rushed in through the unlocked front door -- with sheriff's deputies arriving later.

Moya tells us they found Betsy right away, on the floor of a bathroom near the front door. Their team is trained to spot obvious signs of death, and it was clear Betsy had passed -- so no resuscitation efforts were made.

EMS workers immediately stepped back, waiting for sheriff’s deputies to arrive and take over the scene.

Moya tells us when deputies showed up, they did a full sweep of the massive house. He says it took them a while before they eventually found Gene in the mudroom kitchen.

Moya said Gene was obviously dead too, so no resuscitation efforts were performed.

Moya said paramedics were not aware of pills later found near Betsy's body, or the dead dog in a closet of the bathroom -- and there wasn’t anything unusual other than the bodies.

When Moya's team arrived, they tested the environment for toxic fumes, but meters indicated the area was safe. Nothing came up as carbon monoxide, so they proceeded to walk around inside the home.

Fire personnel performed another check of the home Thursday, as did New Mexico Gas Company workers, confirming the area was safe.

All the info was handed over to the sheriff’s office for further investigation.

Santa Fe County Sheriff Adan Mendoza told "TODAY" this morning the couple may have been dead for days, possibly even weeks.