The Rover-Landers of BC

I just got my '74 series 3 running on the road and I have noticed that the fuel guage doesn't register any fuel although the tank is full. When I drive along even the slightest of bumpy roads the needle flutters about a 1/4 inch on the empty. So do I begin by checking the connection on the fuel guage then check the sender unit afterwards?
I have no garage so I usually find a grocery stores underground or covered parking so the less searching I have to do the better.
Appreciate any advice or suggestions....

The first step would be to see if there is any 12 volt supply at the gauge on the back of the instruments. If there is 12 volt supply the next step would be removing the green wire at the fuel sender unit on the tank and earth it to the body — if working the needle on the gauge will move to the “fullâ€