Point of No Return

When you say "clicks" describe this more specifically...........

Is there one huge CLUNK sounds like the starter solenoid is pulling the gear in, but won't motor over?

Is there one "light" click "might be" the starter relay you hear?

Or is there a clickety...clickety buzzety.... sound?

With no more info, I'd put a meter on the starter stud, and yes, it might be tough reaching down there..........and see what you have for voltage when cranking, and "if you can" catch it when the problem appears, what voltage at that point then

I do hope you have used a "real" battery post cleaner and cleaned up the cables and posts