Ok, here is my hack at it. You will need to build the part inside the dot-dash box as a small shielded module, like in
an Altoids tin. There are four connections to the outside, dbw, Pwr (switched 12Vdc via the Ignition Switch), rly (to 12V relay coil), and Gnd.
The circuit has a high input impedance, so should not load the dbw signal. A 1 MegΩ
TrimPot (U3) is used to set the trip level, which can be adjusted from about 1V to about 4V. The circuit has about 10% hysteresis (drop-out voltage lower than cut-in voltage) to prevent chatter. U1 is a
8pin minidip version of the LM555C timer chip.
The relay U2 can be one of the
automotive 12v "Bosch" type, with a normally-open contact. Note that the power to the circuit should come from the key-switched 12V. The power to the flapper should come separately from the main battery bus (not through the key switch), and should be fused as required as shown by X1.
Here is the schematic and simulation: The lower plot pane shows V(rly) switching as a function of V(dbw) and the pot setting at 0% (green) , 20%, 40%, ..., 100% (grey). The cursors show the cut-in 1.25V and cut-out 0.74V with the pot wiper set to the top pot terminal.