I had a 78 parts car that had a similar problem. I'd get click-whir, click-whir until it finally grabbed and would start the engine. When I finally took it apart I found chipped starter teeth. I don't know if they were the cause or a result, but I have that engine and flywheel in my car now with a different starter and no problems. If you want to test the starter solenoid wiring, make sure the transmission is in neutral, take a screwdriver or wrench, and touch it to the main lug on the starter (where the battery cable connects) and the small male connection on the solenoid. That will provide full power directly from the battery through the tool to the solenoid. If the car is in gear it will jump forward so be careful. I also had a starter begin to fall apart. The bushing in the nose had worked its way out of its seat. That starter made a terrible noise sometimes after starting as the shaft wobbled around. I imagine that it if it had broken or came all the way out, the shaft could have got misaligned and caused worse problems. The starter has a mechanical lever and pivot action from the solenoid to the gear drive. Could be that it just broke.