Thanks everyone for the responses. I tried to solder that original wire and it would not take the solder, as mentioned above. I spent a lot of time and took a lot of care while trying to get the wire back in place. The bottom plastic holder eventually melted with the heat. I finally gave up and ordered a new sending unit. Bummer, since the rest of the unit was perfect. Looked brand new. I now am hopeful I do not need to add a ground wire to the instrument cluster as well, so that I can once again tell how much fuel I have. On to the next project. Thanks.
I would still add an extra ground wire to the cluster. You can buy a ground strap at any autoparts store for like $4, place it between the screws (metal to metal) on the cluster, and run it to the bolts that hold the steering column jacket to the chassis.
Easy insurance because the grounding in the cluster is questionable at best. Nothing is worse than dancing with gauges.