The UAP/Light came from above and stopped/hovered near FL37, about the same altitude as the aircraft, shone a light on the 767 and briefly approached the aircraft. Then it instantly matched the speed, and heading of the aircraft and maintained a consistent separation.
a. The light descended vertically, stopped abruptly, and shone a light on the 767 causing the crew to believe that there was another airliner on a collision heading with its landing lights on.
b. It changed direction from vertical descent to a sudden stop/hover, to approaching the aircraft briefly, to taking the same heading and speed of the aircraft at about the same altitude and an estimated distance of 1-2k ft.
c. It matched the altitude, speed, and heading of the aircraft, 575mph and at 37,000ft for over 32 minutes.
d. The UAP/Light changed colors and turned away from the aircraft on a perpendicular heading, West, just inside the Mexico/US border.
e. The UAP/light did not have wings or running lights. It was a new and unique observation to the experienced air crew.