Yeah, I'm aware of how they work. My point is that the reqs in #1 sound like this to me:
Assuming the resistive sensor is biased with a fixed resistor to either +12 or GND. This changes the direction the resulting node voltage moves in as the tank empties, but it still is a simple fixed/variable-resistor voltage divider. As such (and because of the voltage direction ambiguity), I'll phrase things in terms of resistance value rather than voltage.
1. Below 40 ohms >> relay is "triggered" (continuously energized)
2. 40 to 90 ohms >> Relay stays on
3. Above 90 ohms >> Relay is turned off (de-energized)
4. 90 to 40 ohms >> Relay stays off
5. Below 40 ohms >> Repeat
Maybe i'm reading in things that are not intended by the TS, but to me it sounds like either one comparator with a large hysteresis window or two comparators and a flipflop. If you scaled the voltages just right, you could use a 555.
Note that because we don't know what the relay does, we do not know if there is any feedback between the relay contacts and the sensor, such as a fuel pump. I'm assuming that there is, call it an experience-based guess.
ak