erwabo,
Unfortunately, it doesn't work quite that way. Increasing the mAh of the battery pack only increases the capacity of energy stored, but doesn't begin to change how that energy is delivered. Your circuit of fuel + bias resistor +unlit LED will draw just as much current from a 1000mA battery as a 10mAh battery . . . it will just draw it longer from the bigger pack.
̶R̶u̶n̶n̶i̶n̶g̶ ̶a̶ ̶q̶u̶i̶c̶k̶ ̶a̶n̶a̶l̶y̶s̶i̶s̶,̶ ̶s̶o̶m̶e̶ ̶o̶f̶ ̶t̶h̶e̶ ̶n̶u̶m̶b̶e̶r̶s̶ ̶a̶r̶e̶n̶'̶t̶ ̶l̶i̶n̶i̶n̶g̶ ̶u̶p̶ ̶.̶ ̶.̶ ̶.̶ ̶Y̶o̶u̶ ̶s̶a̶y̶ ̶t̶h̶e̶ ̶f̶u̶e̶l̶ ̶m̶e̶a̶s̶u̶r̶e̶d̶ ̶r̶o̶u̶g̶h̶l̶y̶ ̶2̶0̶0̶ ̶o̶h̶m̶ ̶(̶I̶'̶m̶ ̶a̶s̶s̶u̶m̶i̶n̶g̶ ̶t̶h̶a̶t̶'̶s̶ ̶w̶i̶t̶h̶ ̶n̶o̶t̶h̶i̶n̶g̶ ̶e̶l̶s̶e̶ ̶c̶o̶n̶n̶e̶c̶t̶e̶d̶ ̶a̶n̶d̶ ̶a̶ ̶f̶u̶l̶l̶ ̶f̶u̶e̶l̶ ̶t̶a̶n̶k̶
̶ ̶a̶n̶d̶ ̶y̶o̶u̶'̶r̶e̶ ̶u̶s̶i̶n̶g̶ ̶a̶ ̶b̶i̶a̶s̶ ̶r̶e̶s̶i̶s̶t̶a̶n̶c̶e̶ ̶o̶f̶ ̶2̶7̶0̶ ̶o̶h̶m̶ ̶a̶n̶d̶ ̶a̶ ̶7̶.̶4̶v̶ ̶p̶a̶c̶k̶ ̶.̶ ̶.̶ ̶.̶ ̶a̶l̶l̶ ̶c̶o̶n̶n̶e̶c̶t̶e̶d̶ ̶i̶n̶ ̶s̶e̶r̶i̶e̶s̶ ̶w̶i̶t̶h̶ ̶a̶ ̶r̶e̶d̶ ̶L̶E̶D̶,̶ ̶a̶n̶d̶ ̶I̶'̶m̶ ̶a̶s̶s̶u̶m̶i̶n̶g̶ ̶y̶o̶u̶'̶r̶e̶ ̶c̶o̶n̶n̶e̶c̶t̶i̶n̶g̶ ̶y̶o̶u̶r̶ ̶D̶-̶s̶e̶r̶i̶e̶s̶ ̶v̶o̶l̶t̶a̶g̶e̶ ̶a̶c̶r̶o̶s̶s̶ ̶t̶h̶e̶ ̶f̶u̶e̶l̶ ̶t̶a̶n̶k̶.̶ ̶ ̶ ̶
̶
̶R̶u̶n̶n̶i̶n̶g̶ ̶t̶h̶e̶ ̶n̶u̶m̶b̶e̶r̶s̶,̶ ̶t̶y̶p̶i̶c̶a̶l̶ ̶v̶o̶l̶t̶a̶g̶e̶ ̶d̶r̶o̶p̶ ̶a̶c̶r̶o̶s̶s̶ ̶a̶ ̶r̶e̶d̶ ̶L̶E̶D̶ ̶i̶s̶ ̶a̶b̶o̶u̶t̶ ̶1̶.̶8̶v̶,̶ ̶s̶o̶ ̶t̶h̶a̶t̶ ̶l̶e̶a̶v̶e̶s̶ ̶5̶.̶6̶v̶ ̶(̶7̶.̶4̶-̶1̶.̶8̶=̶5̶.̶6̶
̶ ̶t̶o̶ ̶d̶r̶o̶p̶ ̶a̶c̶r̶o̶s̶s̶ ̶y̶o̶u̶r̶ ̶b̶i̶a̶s̶ ̶a̶n̶d̶ ̶f̶u̶e̶l̶.̶ ̶ ̶U̶s̶i̶n̶g̶ ̶v̶o̶l̶t̶a̶g̶e̶ ̶d̶i̶v̶i̶s̶i̶o̶n̶,̶ ̶a̶ ̶2̶0̶0̶ ̶o̶h̶m̶ ̶r̶e̶s̶i̶s̶t̶a̶n̶c̶e̶ ̶w̶i̶t̶h̶ ̶a̶ ̶2̶8̶0̶ ̶o̶h̶m̶ ̶b̶i̶a̶s̶ ̶w̶i̶l̶l̶ ̶d̶r̶o̶p̶ ̶4̶2̶%̶ ̶o̶f̶ ̶t̶h̶e̶ ̶v̶o̶l̶t̶a̶g̶e̶,̶ ̶o̶r̶ ̶2̶.̶3̶v̶o̶l̶t̶s̶ ̶-̶-̶ ̶t̶h̶a̶t̶'̶s̶ ̶n̶o̶w̶h̶e̶r̶e̶ ̶n̶e̶a̶r̶ ̶t̶h̶e̶ ̶0̶.̶5̶v̶ ̶y̶o̶u̶ ̶r̶e̶p̶o̶r̶t̶.̶ ̶ ̶
̶
̶I̶f̶ ̶t̶h̶e̶ ̶f̶u̶e̶l̶ ̶t̶r̶u̶l̶y̶ ̶i̶s̶ ̶a̶r̶o̶u̶n̶d̶ ̶2̶0̶0̶ ̶o̶h̶m̶ ̶w̶h̶e̶n̶ ̶f̶u̶l̶l̶,̶ ̶t̶h̶e̶ ̶5̶.̶6̶v̶ ̶l̶e̶f̶t̶ ̶o̶f̶ ̶t̶h̶e̶ ̶7̶.̶4̶v̶ ̶b̶a̶t̶t̶e̶r̶y̶ ̶s̶h̶o̶u̶l̶d̶ ̶b̶e̶ ̶m̶o̶r̶e̶ ̶t̶h̶a̶n̶ ̶e̶n̶o̶u̶g̶h̶ ̶t̶o̶ ̶t̶r̶i̶p̶ ̶t̶h̶e̶ ̶2̶0̶m̶A̶ ̶c̶u̶r̶r̶e̶n̶t̶ ̶t̶h̶e̶ ̶L̶E̶D̶ ̶n̶e̶e̶d̶s̶ ̶t̶o̶ ̶l̶i̶g̶h̶t̶ ̶(̶w̶i̶t̶h̶o̶u̶t̶ ̶b̶i̶a̶s̶,̶ ̶2̶0̶0̶ ̶o̶h̶m̶ ̶w̶i̶l̶l̶ ̶d̶r̶a̶w̶ ̶r̶o̶u̶g̶h̶l̶y̶ ̶2̶8̶m̶A̶
̶.̶ ̶ ̶
̶
̶P̶e̶r̶h̶a̶p̶s̶ ̶a̶ ̶q̶u̶i̶c̶k̶ ̶s̶k̶e̶t̶c̶h̶ ̶i̶s̶ ̶i̶n̶ ̶o̶r̶d̶e̶r̶?̶ ̶ ̶P̶e̶r̶h̶a̶p̶s̶ ̶a̶ ̶f̶e̶w̶ ̶p̶i̶c̶s̶?̶ ̶I̶ ̶c̶a̶n̶ ̶s̶e̶e̶ ̶w̶i̶t̶h̶ ̶t̶h̶o̶s̶e̶ ̶n̶u̶m̶b̶e̶r̶s̶ ̶w̶h̶y̶ ̶t̶h̶e̶ ̶L̶E̶D̶ ̶w̶o̶u̶l̶d̶n̶'̶t̶ ̶l̶i̶g̶h̶t̶,̶ ̶b̶u̶t̶ ̶n̶o̶t̶ ̶w̶h̶y̶ ̶t̶h̶e̶ ̶t̶e̶l̶e̶m̶e̶t̶r̶y̶ ̶i̶s̶ ̶r̶e̶a̶d̶i̶n̶g̶ ̶s̶o̶ ̶v̶e̶r̶y̶ ̶l̶o̶w̶.̶ ̶ ̶s̶t̶r̶a̶i̶g̶h̶t̶e̶n̶i̶n̶g̶ ̶o̶u̶t̶ ̶t̶h̶a̶t̶ ̶m̶a̶y̶ ̶t̶e̶l̶l̶ ̶w̶h̶e̶t̶h̶e̶r̶ ̶y̶o̶u̶ ̶j̶u̶s̶t̶ ̶n̶e̶e̶d̶ ̶t̶o̶ ̶r̶e̶d̶u̶c̶e̶ ̶y̶o̶u̶r̶ ̶b̶i̶a̶s̶ ̶c̶i̶r̶c̶u̶i̶t̶ ̶.̶ ̶.̶ ̶.̶ ̶o̶r̶ ̶a̶t̶t̶a̶c̶h̶ ̶a̶n̶o̶t̶h̶e̶r̶ ̶c̶i̶r̶c̶u̶i̶t̶ ̶p̶a̶r̶a̶l̶l̶e̶l̶ ̶t̶o̶ ̶y̶o̶u̶r̶ ̶t̶e̶l̶e̶m̶e̶t̶r̶y̶ ̶t̶o̶ ̶t̶u̶r̶n̶ ̶o̶n̶ ̶a̶n̶ ̶L̶E̶D̶.̶
Edit:
OK, Nevermind. Thanks for the drawing.
remove the 270 ohm resistor and replace with a 100 Ohm Potentiometer. connect the wiper to the "full" fuel sensor and one leg to the LED. fill the tank and turn the pot until the LED lights.
*** KEEP IN MIND ***
As your battery drains, the voltage drops and the LED might no longer light because the battery voltage has dropped.