Can I give an input to the switch manually?

I don't know I expressed my curiosity to the topic well...

I have a mini fan, and I want to switch it with Arduino(photo attatched: fan PCB).
But instead of controlling the motor itself with Arduino, I just want to give an switch 'SIGNAL' only.

I think I can achieve it by giving a small current to the correct pin of the switch with Arduino, but is it actually possible?

Not possible unless the circuit is open source.

You could attach a pair of wires to either 1&4 or 2&3 on your picture. The wires would go to the outputs of an ordinary opto isolator like 4N35. An Arduino digital output would be connected to the opto isolator input.

Whether an opto coupler would work depends on the current the switch handles and whether the circuit
expects the voltage across the switch to drop to very small values or not.

Basically without the circuit diagram the answer is "maybe, maybe not".

It won't work the way you think, but you can maybe do it with an optocoupler or definitely do it with a relay.

But it sounds like you first need to learn about how circuits work. Start with something like why light bulbs need two wires.

@OP, did the same thing with a camera, works well. Used a 150ohm resistor and a low cost PC817
It needs +-25mA though

BUT: measure the current going through the button and the voltage across the button, when it's not in saturation. & check it with the datasheet