Gas gauge calibration unit
It is simple.The circuit measures the sender resistances empty and full. By clicking the buttons, you drive the gauge to read empty, when tank is empty, and full, when full. Not hard, E clicks decrease gauge reading, F clicks increase. On exit the cal values are saved.
No need to calculate. No magic involved. It simply spans sensor travel to gauge travel. As long as the sensor resistance changes with travel, and the gauge can move from empty to full it will work. The gauge can be driven more if needed, because the sender is no longer in series. It can also drive gauge with zero, where the sender would have been feeding with about 70 Ohms.
The circuit values are on the schematic. Component values are not very critical, the calibration resolves those errors.