power from ign sw to gauge is pink - green wire to sender is ground, varied by the sender, so yes you should get a voltage reading there from the terminal [green wire end] to engine ground ... with the wires reversed the guage would likely just read backwards .... when the key is turned on, the gauge should twitch up slightly from the left side [cold] - if you take the wire off the sender and touch it to ground the gauge should go to hot .... I'm not sure a ground anywhere would a problem .... not sure what white resistor you mean, but if that's the ignition resistor on the firewall, nothing to do with gauges .... short answer, if you have power to the sender [voltage reading from sender terminal to ground] it should be working, so suspect the gauge
you can check the sender [new one could be defective] with an ohmmeter, although I'm not sure what the particular values would be, resistance should change cold [high resistance?] to hot [low resistance?], best check would be off engine using flame or boiling water to see change
Bill