Hey Andrew,
Ok, let me help a bit with the meter types and settings. When I do restoration work on the Mopar muscle car electrical parts, I like to use an analog (needle sweep) meter. When using a digital meter on these parts, especially when trying to measure moving resistance readings, it is so much easier to see with an analog meter. When trying to measure moving resistance readings measure right up there with trying to read the actual price of the amount of gasoline you are filling at the pump. The reading is constantly updating and becomes very hard to see.
I am attach a couple of pictures showing the two types of meter settings and readings. The analog meter is set to read Ohms with the adjustable multiplier set to one. You can see I am reading the fuel gauge between - 19 to -20 Ohms. The digital meter is showing -12.4 at 200. If I run the multiplier up to 2K, I do see a similar reading as you have shown, .012 Ohms.
The whole purpose of measuring the fuel gauge by itself is to see the condition of the fuel gauge working or not working properly. Trying to see if there is a short or the fuel gauge is being grounded inside. With your measurement of each terminal on the fuel gauge to chassis ground is not showing a reading is a good thing and does not sound like your fuel gauge is defective.
Jim