Wouldn't you just connect the resistors across the gauge terminal and ground? A 15 ohm should make the gauge go to about mid scale, a 30 ohm should indicate full, and shorting the terminal to ground should show empty. Aren't you just simulating the sender?
Yes, three 15 ohm resistors simulating the sender at empty, 1/4, 1/2, 3/4 and full.
A 10 pack of 15 ohm resistors can be had for under $5 on Amazon.
With the key on the first test is does the gauge read full or more when the sense wire is removed from the sending unit and empty or less when the sense wire is touched to ground?
If no to either, the wire or the gauge is bad or the gauge isn't getting voltage from the battery. No sense going further until that problem is fixed.
If yes to both the wire is good and the gauge is working somewhat, so continue testing. Work the image below from left to right and you only need 3 resistors.
