Why does this timer not work?

Questions & Answers
1

private var currentTime = 0;

function Update (){
    if (Input.GetAxis("Fire3")){
    currentTime = currentTime + Time.deltaTime;
}
   Debug.Log(currentTime);
}
2

You have to press third mouse button then only it increment currentTime value.

First you have to place

currentTime = currentTime + Time.deltaTime;

out side any of the if statement and check whether it increment or not.
Also one more update, change your currentTime variable type to float not var.

3

If you want to check only when the button is pressed to add to counter when the button goes down then use:

 if (Input.GetButtonDown("Fire3"))

If you want to check if that button is pressed for each frame then use:

if (Input.GetButton("Fire3")