Boy, this sure sounds familiar.
Before you go to the expense of a new starter, make sure that your ground cable is well grounded.
I replaced both cables on my '92 a few years ago. Same symtoms. The starter would randomly "click" when the car was started.
I purchased Ford cables because each cable has so many connections on it. If I remeber correctly, the ground cable is connected to the block, frame, and the right inner fender. Any corroded connection at any one of those locations can cause the symptoms you're describing.
Both cables from Ford were about $100, I don't no of any aftermarket cables that would fit that would be any cheaper.
My $0.02.