There is a pulsation dampener (a resistor actually) that bridges the two opposing coils. It's function is to control the rate of movement of the ray (needle) when the sender is generating large fluctuations in a short period of time - like going around a corner fast or slamming the brakes on. If the coil is open, or the entire ceramic plate - on which the coil is mounted - is missing, the gauge will bounce around violently.
Some images of a gas gauge out of a 1986 K30 to help explain:
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And this from someone who knows more about gauges than I:
Don’t Resist Using The Resistor
For some unknown reason, folks do not like to put the resistor on the back of the gauge; maybe because they lost it or they do not think they need it. This type of ceramic shunt-type resistor was phased in to replace the wire-wound resistor and wafer board found on earlier models. The wafer board isolated the resistor from the gauge housing. They both do the same thing by controlling how fast the needle sweeps across the gauge. Think of taking a turn in your Chevy and the needle moving every time! This makes it tough to get an accurate fuel level reading. If the resistor is not in place on an original or AC Delco replacement gauge, the gauge will not operate properly.