On impulse, I almost posted that the AOD did not come out until like 81 or so, and that someone had obviously changed your tranny out...
Well duh... you did say 3 speed didn't you?
Sometimes I am a dumbass....
Anyway, there was a time when old "add on" (factory and dealer installed) overdrive units were pretty popular, I want to say that they would have been getting kinda rare by 63 though. Rare enough that I have never actually seen one in person.
I am trying to say kinda rare but not really "valuable rare", but for sure "cool rare", I would sport it proudly no doubt.
I THINK you will find it is a little "bolt on" unit on the back of the tranny.