Do the other gauges work?
Often when problems appear when started from one station but not the other it has to do with the 12V supplied by the accessory or ON circuits from the key switch, possibly via a relay. So, you might start out looking for a good 12V.
Beyond that, see which brand and, if possible, model of sender and gauges are involved. Often these things are just a variable resistor as a sender and two ohm meters as gauges. But, as this thread itself demonstrates, that isnt always the case.
Regardless, it is often the case in these circuits that one bad gauge or bit of wiring can disable both stations.