‘66 Barracuda Fuel Gauge Pegged!

OK that wire is nichrome. Solder wont stick to it. Its yellowish spiral wound fiber insulation was nearly invisible. The black carbon build up makes it look several times its original size. That restricts beam movement like a plaster cast on arm. Try to clean it and it crumbles to look like black pepper, wire shorts to beam (if it hasn't already).
Buy a good used gauge or send that one out for renew.