You have to see the tail. In its day it was the iconic airliner. Mad Magazine did a bit on "updated" constellation names, and Cygnus the Swan became Constellation the Constellation ... very witty.
I wish I had! Never thought to stop and walk back to the pad. For it's size, black nose and lack of activity, I thought it might have been a T33.
You're right though about the tail, would have known right away even though I didn't know of the 'Baby Connies'.