When the brakelight switch smoked it was trying to carry current that the ground side of the starter circuit was not doing.
Harold is absolutely right about checking for faulty grounds, especially on a car that's sat in storage, but I think we might be putting the cart before the horse.
I'd hazard a guess that the car's sat a while, it's now spring, humidity is going up, you probably stepped on the brake pedal, knocking some corrosion loose in the switch, which caused your short.
I doubt if it had anything to do with the ignition - Keep in mind, brake lights go on even if the ignition is off.
Was it while you were cranking the engine or with the ignition on, that the brake wire smoked? Did cranking the engine facilitate the short? Did turning on the ignition cause the short? I doubt it.
First off, if the engine turned over, you have the battery hooked up right - it's DC current, and if the current was flowing in the wrong direction, the best you could hope for would be a starter motor turning backwards, which would not engage the Bendix drive on a Ford.
Secondly, those old fruit jars tend to get corroded pretty easily - and brake fluid is among the most caustic chemicals used in a car. I've owned a 62 T'Bird, a 66 Cyclone, a 65 Galaxy and a 66 F100, all with the same type of master cylinder, and I had to replace the switch on all of them.
If you are like me, you might have gotten in the car and hit the brakes while settling in. If the switch was compromised, ie, at one time got some brake fluid in it during servicing, was damaged and/or corroded - not unusual for an old Ford (or take it from me, anything British), this action might well have shorted out the switch internally and started smoking the wire. It would take a few seconds for the wire to start to smoke, which would coincide with your efforts to crank the engine. I suspect the two events are unrelated.
I'd check to see if the brake lights are working - you should be able to simply short the two switch connectors together through a 10 amp fuse to see if the brake light circuit is good. Do this through a fuse, because if there is a short in the brake circuit, you don't want to have to pull a new wire through the Galaxy unless absolutely necessary, which is what you'll be stuck doing if it burns through. If the lights work, then your switch is probably faulty. Make sure you haven't already burned the fuse in the fusebox.