The passenger side is usually for a vacuum switch like a DS-TVV or a DS-TVS. But it depends on your model year and engine. You could put the temp sender in that location but it should be between cyclinders 1 and 3.
Isn't it just a joy to find cut wires? :evil: It would have been just as easy to fold them up and stuff them in the plastic wire coil.
I think you can get the connectors for the senders at your parts place too. So you could rig up another wire and run it to the gauge. If you don't want to splice that wire to your existing harness, put a washer type solderless connetor on the end and slip it over the screw at the temp sender location on the back of your cluster. Just leave enough slack to be able to pull the cluster out and unscrew that wire. Or put a bullet connector on the end of the wire from the sender. Then take another wire and use the washer type solderless connector on one end of another piece of wire, and the female equivalent of the bullet in the other....then plug the wires together. That would make it easy to pull the cluster.