Well i wouldn't totally rule out that the second alternator went bad also (been there, done that) but assuming it isn't the problem then the problem is likely in the connector that goes to the alternator. I've worked on Fords where the large black connector (i think your car has two connectors, one small, one large) was bad.
Try bringing it to somebody who can test the alternator in the car and see if wiggling the wires makes a difference. If it does then you've found the problem. If not then see if somebody can test the alternator itself to make sure it isn't defective.
In reality it could be various things such as a bad ground, or other wiring problem.