I reckon you have nailed it Peter, it is a bad connection some where.
I good way to prove it would be just turn on the ignition without starting the car, do this without being in the car as you will cause vibrations. Now stick your head in the car and see if the needle is flickering. If it is not start the car and see what the needle is doing. If the needle is flickering it is cause by engine vibrations.
A good place to start is to have the engine off and the ignition on and lightly tap the dash and see if the needle flickers with the taps. If nothing there you can assume all is good at the gauge end. Now tap at the fuel tank and see if the needle flickers, if it does you can assume the problem is at the sender.