engine temperature indicator
As best I can determine, beside the fuel gauge, the other round gauge with the needle, that for the mostly sits horizontally, is effectively an engine temperature indicator rather than a coolant gauge.
My understanding of the operation of the indicator is that it gets its information from the engine computer and as such, only indirectly from the coolant temperature sensor.
There is also an oil temperature sensor located near the oil filter that feeds information to the engine computer. The reading of the indicator is some combination of the two, the coolant and oil temperatures.
Apparently if the coolant temperature sensor fails, the oil temperature sensor readings are supposed to take over via the engine computer.
Also the engine computer programming is designed to make certain that the needle display always shows nears the middle regardless of engine conditions - assuming the computer regards those conditions as within norms.
This was a service and marketing requirement as apparently a temperature needle that runs at different positions causes owners to hassle the service department with questions as to why the needle position changes. The official term for this "horizontal needle design" is damping.
You may note that most Series LR vehicles, and for that matter, many other vehicles do not have a temperature indicator, only a light that goes on indicating over temperature, or something like that - in other words, it indicates bad news rather than showing a trend to bad news - what ideally a non damped temperature gauge would show.