A rubber piece fellout and there is a white wire hanging out.

This just happened to me.

The waxy piece has a clear plastic bracket, if its not connected, look around your freezer. The waxy piece fits inside the bracket, and attaches to the ice maker, just in front of the ice tray.

The white wire fits inside the waxy piece. It is the thermostat that tells the ice tray when to dump the ice.

This is impossible to feel around for, so you will need to remove at least the bottom freezer compartment as well as the ledge piece from just inside the freezer door. If you are a relatively thin/small person, you can extend the top tray fully outward, and slide underneath. Looking up at the ice maker, the plastic bracket should have a little prong. This prong will attach just behind the ice maker, with the thermostat facing the ice tray.

Here's my description of the same process. Agreed, was unable to find a diagram and it took me way to long to work this out without one. As JCS said, you're gonna need to get in there, I don't think this would be possible to do without seeing.
There are 2 pieces that reattach the sensor. There is a foam-rubber piece that the sensor seats into. There is a channel in it for the wire. This assembly is held into place by a plastic bracket. Before getting in there, make sure you put the three together to see how the fit.
Pull out the top drawer of the freezer. Place the sensor back into the foam-rubber piece. Wiggle your head in to the freezer looking up at the bottom of the ice maker (I'm 6'4" 200, wasn't easy). The foam-rubber piece will slide up behind and underneath the last cube, closest to the door, such that the sensor is making direct contact with the cube. You can then slide the plastic bracket into place. There is a small pin like protrusion on the bracket that will hold the whole thing up. You may alternately try putting the whole assembly in together, but I had worse luck this way.
When you've got it, its still going to be kind of loose, explaining why it fell out to begin with. Really poor design here. Anyway, you should be able to give it a light tug and it won't come out. Make sure the wire for the sensor isn't protruding anywhere that it will snag. From now on, I'll be real careful that ice doesn't build up and rip this off again.