I turn the starter switch several times it will eventually start cranking?

When I go to start it it just clicks if I turn the starter switch several times it will eventually start cranking if I catch it right. Having to start it using a screwdriver at the starter switch but the starter switch is brand new, battery brand new, starter in good working condition been tested and tried alternate starter on car as well to narrow down the issue. All relays are good tested and swapped out to be assured they weren't the issue, since the issue started my radiator fan now turns on as soon as you turn the car to the on position on the starter switch and never goes off regardless of engine temperature. I've checked the wiring I could see and it all seems to be sufficiently grounded connected etc. Any help or advice is greatly appreciated.

Update: the radiator fan constantly running was a separate issue one of the sensor wires running to the fuse/relay box in engine compartment was cut repaired wire and radiator no longer constantly running but had no effect on the no crank/just clicking issue. Again would be if I tried starting it over and over it would "catch" and start cranking sometime just barely though. But spent over 2 hours doing the normal trying over and over as fast as I could and now not getting lucky with it catching at all.