it could be wire off the guage. in those days it was simple. probably two wires to the guage, or a hot and grounded to the body. OR it could be the float mechanism fell apart in the tank or just quit working, stuck, etc. wire from tank COULD be broken off. could be a bad gas guage!
man! i HATE car wiring! takes a lot of following wires, often taped or in plastic tubes called conduit. unless you are blessed with a family car since 1967 and no other owner "fixed" it, wiring can be obscure from too many jumped wires, skipped wires, mal-repaired wires. there are maps of wiring you can google, or a chilton's 1967 mustang
shop manual should have a diagram. a new wiring harness (heck to install) is probably $300 or more. i have a 67 ford pickup project and hope to heck it doesn't have too many "repairs" on electrical!!