If I remember correctly, ESP8266 ADC input range is 0-1V.
What you want to measure is voltage going to analog gauge. I would follow these steps:
- measure voltage with the multimeter when tank is full;
- to be on the safe side, measure the same voltage with analog gauge disconnected, see if it is higher and what the difference is;
- while doing that you might measure resistance of the disconnected gauge, to know what load is seen by the sender in original setup;
- now simply connect a voltage divider between sender signal and ground, and use the output voltage as input to ESP (possibly with some voltage clamping diodes thrown in).
I would use a precision, 10 kOhm multi turn variable resistor (potentiometer) as a voltage divider. They are sealed, so perfect for the expected usage
environment. Simply adjust with full tank, to get around 0.9V output. If input impedance of ESP will alter the reading once connected, simply readjust slightly.