The pick up coil and reluctor are what replace the points in the dura spark and other newer electronic ignitions although unlike the points- the signal needs to be amplified before it can directly trigger the ignition coil by opening the circuit.
I would Make absolutely sure the black ground mentioned earlier is clean and securely grounded- had this same problem at times with some of my old AMC/jeeps- uses their version of the early dura spark and the ground is critical.
It sounds like it could be the pick up coil , seen a few go bad in Amcs and (GMs) to and they are great for driving a long and stranding a vehicle- then the engine cools down and will start right back up like there is no problem - till the next time you get a few miles from home...
Pick up coils produce a weak signal , have always used an oscilloscope to check for output.
Also can't speak for the Ford dura spark- but gms generally require removing the entire distributor and then driving the roll pin out of the drive gear to remove the shaft from the distributor housing before the pick up coil can be removed...
Ps. if the distributor does need removed mark the distributor cap position with something on the engine block and also the rotors position to the housing -( Before removal.) otherwise you will have to find #1 TDC compression and re time the engine.
One other thing as i mentioned earlier some of my AMCs had the early dura spark - but when they failed it has become cheaper to buy a new HEI conversion instead - last one i bought for my 401 v8 was like $50 and came with a high output module and coil with a performance cap and vacuum advance-
the best part- 1 wire + 12 volt hot and you are in business. but not sure if they are available for Fords?