Q: Trying to start the car yields only loud clicks but the battery and starter are good

Bench testing a starter motor, unloaded, can sometimes be unreliable. This is because there is usually a Bendix drive in a starter motor which if failed will be undetectable because the starter motor will still spin and draw normal current- but if once you load the motor, that is involve the Bendix drive, the unit simply will not work, particularly if you have a weak battery. At any rate, that advice mostly applies with relatively "old" starters which may not be the circumstance you face. A certified mechanic would diagnosis your fault by doing a circuit trace and in particular measure the voltage drop from point to point in the circuit. Obviously, there is either an open in the circuit (in a starting circuit, could be a failed contact or relay or a high enough resistance somewhere in the circuit that the resulting voltage drop makes it impossible for a relatively high current motor to run. It could be as simple as a failed solenoid or high resistance ground. If you’d like, YourMechanic would be happy to make a mobile visit and diagnose your car’s inability to start issue for you rapidly.