This is my sacrificial Twist which I tore down when the button got stuck after I dropped it.
Best way is to screw an old carto on and pretend that the twist/carto is a twig that you're going to snap. So you make a fist with a hand at each end and put your strongest thumb against the part where the body and connector meet so it becomes a pivot point and gently rock and pull. I've found putting my fists down on a rag on a bench helps to control it by eliminating one axis of movement.
As soon as you start to see the parts separate like (photo below), reduce the pulling force that you apply as you dont want to snap the wires off when the parts finally come apart. (My first time, I yanked so hard that the connector went flying across the kitchen, hehe
Gently pull all the bits so you can get the button out and end up with this:
The button needs to go in with the flat part towards the front.
Hold it with the button hole facing downward and use a match, drinking straw, pencil to push the button into position.

EDIT: Oops, that one's upside down, but I can't seem to upload the rotated one.
Then push the circuit board into the connector so it sits in the slots and push the connector and body back together. The button originally should be in line with the writing "eGo-C Twist" on the body. I changed that to the opposite side which makes it easy to see the voltage level I'm on without changing my grip. (I hold the twist with my index finger on top pressing the button if that makes
sense.) Anyway, the point is that you can align the parts differently if it suits.
I'm no photographer or teacher, but I hope that helps you fix your button.
