As the investigation into the mysterious death of Gene Hackman and his wife, Betsy Hackman, enters its second phase, following last week’s revelations from an autopsy performed after the couple’s bodies were found in their Santa Fe home, more details are emerging around their health and shifting habits in the final month of their lives from family and close friends of the couple.

Hackman, the two-time Academy Award winner whose Hollywood career spanned four decades, and classical pianist Betsy did not die from carbon monoxide poisoning, Santa Fe’s sheriff concluded on Friday, ending speculation that a gas leak killed the couple, who were found Wednesday in separate rooms of their home during a wellness check; both showed no signs of external trauma, police said, but Hackman’s pacemaker had sent its last record on Feb. 17, suggesting he had been dead for at least one week before his...