Aircraft taking-off seen trailed by two unidentified object / vehicles

I was sky-watching while sitting on my backyard deck (I like looking for satellites or watching aircraft from nearby McGhee Tyson Airport). I have a pair of binoculars that I use during this endeavor.
 On the night of June 15th, 2021, I saw an aircraft taking-off around 2300 hours. It was traveling in an easterly direction, and was about 45 degrees above the horizon, when I focused my binoculars on it. At this time I saw two lights, which looked like what you would expect when seeing satellites, traveling above, and in the same direction as, the aircraft. I then saw each light bank-away from each other, and take-up a position behind the aircraft. It looked like a classic fighter maneuver to get behind an adversary aircraft. The lights "tailed" the aircraft (closely, but not close enough to be a hazard) for a short distance before they both climbed upward at a steep angle. I lost sight of the lights before losing sight of the aircraft.
 Other than the engine noise from the aircraft, no unusual sound was heard. They lights were a solid, white color. They had no other lights that were visible to me (such as collision or navigation lights as should be seen on an aircraft). I do not think they were drones, at least in the conventional/non-military sense owing to their speed and maneuverability.
 I should also mention that I have good knowledge of aviation and aircraft.