The thing that is critical on the Ford "brain boxes", the "connector" where the wires meet the box is a particular color. You need to make sure the replacement box has the same color connector. If it is not it will give you issues like you describe.
Typically if the brain box fails you get no spark whatsoever.
If the vehicle has been sitting that long, rebuild the carb. The gaskets have dried up and no longer capable of sealing.
Is it an Autolite or Motorcraft carb? If a Motorcraft it is a Holley carb. If it ever backfired even once through the carb the power valve is toast, creating a very rich idle condition.
Do check the ballast resistor for the ignition, I don't recall if it is a physical resistor or a resistor wire.

The car does not have enough miles that the issues are going to be a worn out this or that. Look for indicators of critters chewing wires etc.
Good luck, 79 Lincolns are awesome old long noses.