Neko ears project help

Hi im trying to make a project like this
but using an Arduino nano but with the same style of 4 servos

and in hear lies the problem i have no trouble making the hardware parts but my coding skills only allows me to link the servos to a joystick, I would like to be able to program it to almost have a random or pre-programmed amount of movement, so it looks more natural and i don't have to keep my fingers on a joystick the whole time. ideally, id like to make it run off the joystick and by clicking in the stick it will run on "auto" and then clicking it again turns it to manual mode again.

so if any of you could point me in the right direction of where to learn to do that or how i can combine example code that would be very helpful