My brother Mike bought my 86 SE, and left for home yesterday. He stopped overnight in Jackson, MS. This morning, the car wouldn't start. He called me and described the symptoms. I suggested that he change the ignition module (I had included one with the car). He did, and the car started right up.
He told me that he was going to head for the nearest parts store and get another one.
Ah, the joy of owning a Fiero!