Perhaps I am confused as well. Is this a separate car, or are you talking about SteveBones' (the OP) 58 TR3A?
SteveBones said
Control box
A1 Connection - No voltage measure with switch on or not.
Control box -
A Connection - Yes Voltage
This is clearly a problem with the control box (or perhaps the connections to it if he didn't probe directly on the A1 terminal).
There might well be some other problem present, but this one fault would cause all of the current symptoms (no lights, no ignition) as that link provides power to the entire car (except horns and starter).
So my suggestion is to fix this one, and see if that addresses all the problems. If not, then he will need to go through the troubleshooting process again to isolate the other fault(s).
Lather, rinse, repeat. While it's certainly normal for only one thing to fail at a time, I've had several times that there were multiple failures. Sometimes two things fail at once, or sometimes something fails while working on something else. Broken wires tend to fall into the latter category, since things get moved and flexed while working on other stuff.
Might even be related failures. Like maybe (strictly as an example), there was a short in the white circuit (which is not fused) and the weakest point was the A-A1 link inside the control box (meaning it was on it's way out already). But the over-current for the short also overheated the contacts in the ignition switch, which oxidized from the heat until they won't pass enough current to run the ignition.
I'm not saying that's likely, in this or any other case; just that strange things can happen sometimes. The solution is to troubleshoot in an orderly fashion until you identify a fault, fix that fault, then try again.