What is this wire?

Or if you are really desperate, carefully slice the wire connection leg underneath, peel it back, flux it up and solder the wire back on. Some/ many/ most/ all? of those temp sender studs are threaded, so with the addition of a couple of machine nuts, you could put an eye end onto the wire and connect it that way.

Mine broke off, and I tried just that. But I could not find a nut that would thread on the stud. I eventually used one of those sheet metal quick nuts such as are used for badges and lettering. Anyway, I was looking to replace that with a right-angle connector, so I'm glad I found this thread.