OK, I take it your power wire that goes to you coil + terminal is hot when the key is off. If stock it's pink and black in a 68, I think it's orange and purple or orange and blue in a 67 but not sure. Don't know what the 69 is.
The ignition power at the switch is in a pink wire that goes to the K position at the firewall bulkhead connector, and comes out of the K terminal in a pink and black wire on the engine side of the connector, to the coil. If you disconnect the pink/black wire at the coil, and isolate it, and you still have voltage when the ignition switch is in the off position, you may have a defective ignition switch, or the pink wire is connected to the wrong terminal at the switch.
A lot of other ways the pink wire could be getting juice other than that but the wiring would have to be about as bad as mine was when I bought it.
Now you say when you "give this wire constant power", do you mean when you turn the switch to the start position the car starts but when you turn it off it keeps running? Or are you giving it constant power from somewhere else?
That is not the only wire that goes to the coil + terminal. There is also a yellow wire that goes from the starter to the coil +. That yellow wire should only be hot when the starter is in the engaged mode. When the starter is powered from the purple wire coming from the start position on the ignition switch, it closes the contacts in the starter and the yellow wire is energized via the battery cable. That gives 12 volts to the coil when starting. If the starter is defective, or the starter is incorrectly wired to the electrical system, you may, MAY, be getting 12 volts from the battery cable to the + terminal at the coil. Since the yellow wire and the pink/black are both attached to the same terminal at the coil, that could cause power getting through the pink/black wire in the opposite direction from normal.
Kinda a long shot but a possibility.
Oh yeah, don't think that the wiring is new because it looks real nice under the tape, It's surprising how nice the 50 year old wires look when you unwrap that stuff.