The next day...
After the locks on our rental unit were changed, I spoke with the rental agent. She feels quite certain it was one of the "Security" Guard" who came visiting last night. The maids leave their keys with the guards, and the guards have a list of empty apartments. Ours was on the list, since the list hadn't been updated after our change of plans. The guards have been known to visit empty units to watch TV or take a little snooze. Of course they're not supposed to do this, but they've been caught at it more than once!
At any rate, I don't expect this incident will affect our ability to sleep tonight, especially since Dick managed to fall back to sleep rather quickly last night!
Post Script -- After an eventless second night, a knock on the door woke us at midnight the third night!
It was the security guard. He was doing his rounds and noticed our air conditioning was still on. This is not permitted after midnight. I wondered: Was this a new security guard or the same one who visited the other night?