Sounds like someone wired to the wrong terminal. There is a relay that the power window main feed goes to and another wire to the fuse box, on a switched terminal. Once the switch is on, the relay makes contact and powers the windows. I am not sure where the relay is on a 66 but on 68-72, it is on the drivers side under the kick panel.
The windows are supposed to work with the ignition off on a 66.
As far as I know, all GM cars from 67 on back worked that way.
Kinda nice not having to turn on the key to put the windows down.
That's why they changed it, too easy for theives. i think they changed it right around when they came out with the locking steering column.
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