Symptoms you describe are the same as I've had with three different cars over the years.
In each case , after lots of hunting and testing the fault was eventually diagnosed back to faulty starter motors.
They would start OK if battery was absolutely charged to full capacity but as soon as battery was just a little below top notch -----a lot of solenoid clicking but no starter rotation.
Replacing the starter motor was the remedy on each occassion.
Hope you find a cheaper / easier cure.
In each case , after lots of hunting and testing the fault was eventually diagnosed back to faulty starter motors.
They would start OK if battery was absolutely charged to full capacity but as soon as battery was just a little below top notch -----a lot of solenoid clicking but no starter rotation.
Replacing the starter motor was the remedy on each occassion.
Hope you find a cheaper / easier cure.