I kept the plastic base. No need to "wrap" the leads, just bend one to touch the smaller spring and the other on the opposite side in a way that it touches the outer spring.
The smaller spring touches the battery lead at the positive end of the battery. The larger spring touches the body of the light to act as the ground.
One lead touches larger spring
Other lead touches smaller spring
This one is fugly, but another one turned out nice but leads could not be seen by the camera.
Mutt light
Solar Force head, fivemega body, Laser Products tailcap.