On your 1961 it is very easy. When the float is at the bottom, the ohm reading should be close to 0 (choose 0-200 ohms on your meter or just ohms if your meter auto-selects the range). When the float is at the top, the ohm reading should be 30 or close to that. As you move the arm slowly while the meter is connected (one lead goes to a good ground source or the body of the sender unit and one lead goes to the center screw where the fuel gauge wire connects) the reading should range between 0 and 30 ohms. Ohms as you may already know are units of resistance. Please let us know if you have questions.
If you know any friends who are electronics hobby-type guys or gals, ask them for a 10, 15 or 22 ohm resistor. Those are crazy common and anyone who tinkers with circuits ought to have several around. Then it becomes really easy. Remove the center nut on the sender, remove the wire and with the ignition in the on position, hold one side of the resistor to the connector of the wire and ground the other end of that resistor. Don't worry...you won't get any sort of shock. If you have a 10 ohm resistor, your fuel gauge should read about 1/3 full. A 15 ohm resistor should give you about 1/2 tank reading and a 22 ohm resistor should give you about 2/3 tank full reading. If that doesn't happen, and if your sender seems to be working (incredibly unlikely if you have the original sender), then something has happened between the tank and the gauge.