1994 Oldsmobile Cutlass Starting

When starting my car, the starter makes a whining noise. Some days I will go to start the car and it will just "click" one time. Then I will turn the key a second time, sometimes a "click", sometimes she fires up with that whining noise (from starter). Have replaced battery and starter (including solenoid), within the last year and problem has persisted.

I have had my girlfriend start the car with me under the hood and it seems to be coming from the starter motor itself. Tried multiple shim options, same result. Could this be a faulty wiring issue? If so what wires do I test? I do have all tools necessary to make repairs.