The black wire on my Uego Wideband was pulled from the back of the plug, sensor side of the gauge wire. (so if you have Gauge, wire, plug 1, plug 2, wire, sensor. Plug 1 and 2 go together. The wire was pulled out of plug 1)
(G)-----[1] [2]-------(S)
Inside the plug are the receiving pieces for plug 2's prongs. I believe I have to remove the prong to reconnect the wire, but I do not know how. I tried getting a needle nose on it from the front side, but I'm afraid of damaging it (already bent the lips in a little)
I don't have a camera with me, but I'll try to google a picture of the plug style.
*edit* It's not a great shot, but it's the plug at bottom center of this photo.