Usually the fuel and water temp are
bi-metal current gauges (in older cars)...that is they are a bi-metal strip with a coil of wire around this strip.
As I is passed thru the coil the bi-metal heats and deflects..which then moves the fuel pointer.
Thus Voltage for these gauges must be stabilised as I is a function of Voltage. There must be a regulator for these instruments.
However that said..these regulators are usually for the fuel and water temp..not the speedo etc...that I know of..so it is more than likely the V supply to this that is being lost.