Here's a couple of images from the parts catalogue.
The first pic is the Fuel Distribution Module. This unit sits inside the fuel tank and incorporates the fuel level float (the ball).
The second pic is rotated to show the relationship of the Fuel Distribution Module to the tank. The bottom of the unit would sit on or near the floor of the tank. The float arm does not reach the highest point of the tank because the mounting plate is below the top of the tank.
Speculation follows. I don't know the specifics of the IA level system so this is derived from these two images plus knowledge of tank quantity indicating systems in general. I might be completely off the mark.
The fuel tank has a top bulge at the rear and a sloped floor at the front. The progression of the fuel gauge from top to bottom will not be linear unless the gauge is programmed for the tank profile per
@Bobcatbob's question. Based on my own observations of the gauge behaviour I think it's a simple linear system.
When the tank is at or near full the float will be in its highest position but below the surface of the fuel. The fuel in the top portion of the tank needs to be consumed before the level drops enough to bring the float into operation. That would explain why after filling the tank the fuel gauge takes some time (distance) before it moves. The gauge does nothing for the first x miles/km because during this time the float is submerged and outside its operating range. That would also explain why the remaining range when full shows 'greater than x' rather than a specific distance when the tank is full. When the fuel level is higher than the float the trip computer knows you have
at least x miles/km remaining range (based on the averaged recent consumption rates) because there is more than x gallons/litres below the float in the highest position. Until the float comes into play, the trip computer does not know the exact fuel level to be able to provide a better range estimate.
The Fuel Distribution Module is installed towards the rear of the tank. The tank is generally rectangular with the long sides aligned to the chassis. At lower fuel levels, perhaps 75% or less, that will make the fuel gauge sensitive to vehicle pitch angle. Pitching down sends the fuel towards the front of the tank and away from the float so the float drops. Tanks are typically baffled to reduce the rate of fuel movement within the tank and gauges are electrically damped to reduce the change rate sensitivity, but if the vehicle remains pitched (parked) nose down for any length of time the fuel gauge will indicate less than the actual remaining fuel level because the float cannot sense the higher fuel level towards the front of the tank. This error will self-correct when driven back onto a flat surface.
None of this is unique to Grenadier, but are common artifacts of system design that can make fuel quantity sensing systems unreliable at times depending on the tank shape, fill level and vehicle angle.
