if the gauge is reading low it is either one of two things; the thermostat is faulty or the temperature sender for the gauge is defective.
Run the engine until warm, the radiator hoses should be about the same temperature. if one of the hoses is considerably less or even cold then suspect the thermostat. If they fell the same then I would suspect the temperature sender unit
no not really. they work independently form each other. Unless there was a problem with the circuit board for the gauges, but it would affect more than just these two gauges.
I would check the hoses to see if one is colder than the other.
Does the gauge ever move at all or does it stay on full cold?