Okay, I know yours is 16 years newer than mine, but some things don't change much.
The starter has a solenoid on it. You said it was bench tested and good. Unlike Fords, the GM starter solenoids are attached to the starter. In addition to that starter solenoid, they put another solenoid in the circuit because apparently there were re-start issues (starter would run on its own after starting). So there are 2 solenoids - at least that's the case on my '84. The second solenoid is mounted to the alternator bracket. If it fails, it won't send juice to the starter.
The clicking sound could be just about anything. Like wa8yxm said, different sounds mean different things. The click you hear could be the start relay.
All that said, I'd still suspect the starter itself.
1984 Allegro M-31 (Dead Metal)