The APU could have been running, but it's not normally done.
Contrails can also form (as I guess you know) from wing tips, corners of flaps, etc.. If it was above the other two, it might be from the top of the fin. But these usually occur at low altitude in saturated air, and quickly disperse.
Used to see our own contrails regularly after completing a 70-deg turn over Nice en-route Tripoli many years ago...