Red yellow and blue connect to the indicator, and you apply 24VAC ( probably 50Hz, though this could also be a 100Hz or 400 Hz indicator, limit the current and start with 6VAC as test and a 100R series resistor) to the black wires, and as you rotate the centre it will move the pointer on the indicator to follow it. Simple resolver remote indicator there, the Ac is exciting a coil in the head and the 3 coils are transmitting a 3 phace voltage with a magnitude and amplitude for the indicator that follows the phase of the excitation coil.
Show pics of the back of the indicator, and any manufacturers plate there, that is a really old Smiths instrument, probably made around 1964.