I'd say mechanical; with the key on, the system is energized and the guage is reading what the sending unit tells it. The problem is seldom electrical. You probably have a stuck sending unit in the tank. Find the sending unit port in the top of tank, make sure its connections are clean and tight, same with the connections on the back of the gauge. Take the sender out and move it's sensor arm up and down. The gauge should go from E to F and vice-versa. If the gauge fails to move, the sender is corroded, replace it.