You have 02 things by keeping it Automatic, Right now its working when your Car engine Coolant needs some cooling its OK unless you have some problem in Thermostat or Coolant passage ways otherwise, you need some Electrician help put a Manual Swicth in place as when you want you Fan should not start as soon as Ignition then that Switch should work as Automatic Fan while OFF but when Switch ON it should give Continuous Power to FAN for run by that way you can control it.
There is no variable duration controller for fan turn ON and OFF while its Automatic it depends on Thermostat Switch, half way is actual temperature your car needs