I'm in the middle of troubleshooting the same problem. Mine would fail occasionally and mostly gave me trouble when the engine was hot and recently it stopped working altogether. I think that I traced my problem to a combination of old dirty connections with the worst of them being in the console wiring harness to the neutral safety switch.
The problem is that not enough power is getting to the starter solenoid to activate it. This can be caused by a weak battery or one or more bad connections between the battery and the starter solenoid switch. It can also be a bad connection between the body of the solenoid switch and the negative battery post.
After studying the wiring diagram I learned that the starter solenoid circuit is as follows:
1 fusible link from battery + to terminal post on the radiator support near the battery.
2 wire from terminal post to horn relay
3 wire from horn relay to the bulkhead connector on the firewall behind the power brake booster
4 wire from the bulkhead connector to the ignition switch
5 wire from ignition switch to the neutral safety switch in the floor console (auto transmission)
6 wire from the nuetral safety switch back to the bulkhead connector
7 wire from the bulkhead connector to the starter solenoid
Any and all of these connections can get dirty and cause resistance in the circuit that adds up to a problem. Or as stated previously it could be as simple as a weak battery or bad battery cable connection.
Happy hunting and I'd love to hear what you find, ,Mike.