Escort Wiring Advice

That switch wire could be connected to the solenoid + outlet, not the fat red wire from the battery, the other side of the block, I could be fully wrong as wiring isn't my favorite either.
You said 2 wires on starter so one is just dangling free, have you swapped them over to see if it starts better ?
I have a couple of Wasp reduction starters that are the same with 1 trigger wire, never had a problem

It sounds as though the coil isn't getting power in the ON position? Or, it would have power, when you cranked it, it wouldn't, however you'd finish cranking, power is back at coil and it would only fire because the engine was still spinning?

Check you have voltage at the coil in the ON position. The starter should have 12 volt constant, and then only the trigger/solenoid on crank.

This thread may help.?

https://www.classic-ford....tm.aspx?m=81657&p=

Shaun

late to the party as usual, sorry.
I had the same issue when I made up a test stand to run the pinto on and had to bodge a basic loom from scratch.
I didnt realise, but of course it does, that the coil had no feed no 12V feed to it, so I'd get the engine to turn over, then fire, and when I returned the key off ignition to running position, it'd just stop.
If that was roughly your scenario Drew, then yes, the coil needs a constant 12V feed.
It can come from the back of the starter motor, which since it has the thick 12V feed straight from the battery, its just about always live.
If it's coming via your ignition switch, thats probably better, as it will be fused and not always live either with the car off. So long as it stays on with power once you are in the running position. 
I dont think you need to change the ballast resistor wiring just yet, the missing cable would be more important.
The ballast wire (often pink stripe on grey) just  allows for a full 12V to the starter motor if you need it when cranking.
 

MarkA is spot on, need to have a non resistor coil if you feed direct 12v, the ballast wiring drops the voltage considerably, so it will kill a normal coil quickly.

The ignition has two circuits. Engine start and engine running.

Position three on the ignition switch (start position) uses the red/light blue circuit that supplies 12v to activate the starter solenoid circuit. On the starter there should be a red/light green wire that only receives power when the solenoid is activated by the start circuit. This red/light green wire supplies the coil wire AFTER the ballast resistor direct 12v to start the engine. 

Position two on the ignition switch (engine run) uses the normal ignition circuit, red/light green, which is fused and runs through the ballast wire. Here's some pictures from the wiring diagram below, note the red/light green and red/light blue wires, you can see the join of the red/light green wire pictured just down line from starter, trace that back to the starter motor and you can see how that part of the circuit is only supplied 12v power went the starter solenoid is triggered.

So hard to diagnose these things remotely Drew.
For the testing of the coils, just look at some YouTube stuff. Unlikely to be the problem, especially when cold.
 
Off topic a bit here, but on all my rebuilds I bypass the original Ford ballast resistor wire as they tend to be problematic. Just my experience.
Mark