ClassicCar

Charles, you'll probably read zero or near zero ohms on both the gauge and the sender. The gauges and senders up through 1950 do not work on a resistance basis ... they have a little heater element that heats a bimetallic strip with "make and break" contact points.

You may know some or all of the following, but in case not:

To test the gauge, disconnect the wire from the sender and ground the terminal that connects to the tank sender; if the gauge swings pretty smoothly over to the empty (left) side, it's operating OK (don't keep it grounded that way any longer than needed for the test, or it may be damaged). Test the wire back to the sender by connecting it to the gauge and grounding it at the tank end; you should see the same gauge behavior. If nothing happens, you've got a break in the wire or it's not grounded well. If the gauge is sitting all the way on low, the wire is likely grounded somewhere.

OK, that leaves the sender. With it out of the tank and with the wire to the gauge connected, ground the housing with a jumper wire and observe the gauge behavior as you move the sender arm from one end position to the other. These (King-Seely) gauges can be rebuilt, but it's expensive. "Big Paul" Schuster has replacement sending units. They operate on a resistive principle, but are calibrated to work with the pre-'51 Hudson gauges.