Putting an old ALPS variable resistor push/pull switch

[gkmaia]

I had to put these apart to replace a broken shaft.

Now I am really stuck trying to put them back together. I know the position the black and white bits should go, but the spring is a mistery... how does it fit?

[shakalnokturn]

I've never taken any of those appart and lack detail to guess from your photo.
Most certainly it is there to give some "snap" action, mechanical hysteresis.
I'd expect either tail to fit a small hole, the spring loops must have room to flip over a little less than 180° when moving from on to off position.