the 2 cables should be connected to the cover you have pulled off, its hard to tell from the pic but that top wire looks like it should be connected to the metal terminal on the cover which is at the bottom of the pic.
yea mate thats why the wires are there, they go inside to the switch, so if you hook up the wires you should be able to push the button without the pad being clipped back in
had a quick look today, i can find the connectors/pins for the plugs on the detachable face, but theres one wire that i cant find the connector on the wheel end. it was juts forced into a metal hole but that clearly wasnt working. if you look at the photo above with the wire thats hanging free, the wheel-side end is just wedged in there, not connected to anything.