The senders are often suspect. If the wire's connection to the sender is secure, I'd suggest replacing the sender. They're a little tricky to access - the nut is on the back side (either 14mm or 17mm) with little room for a wrench. I use a cut down bicycle wrench. They're stamped out of 1/8" thick steel so easy to cut or bend to fit. Once you get the sender to turn 1/4 to 1/2 a turn it'll come off by hand.