If the display function does not work, replace the meter unit.

Check 3-6: Neutral Indicator Light (LED) Inspection
Meter Unit Circuit (ZX1000J Model)ESD (Electronic Steering Damper) ECU Removal (ZX1000JD/KD)
NOTICE
Never drop the ECU especially on a hard surface.
Such a shock to the ECU can damage it.
Lift up the front portion of the fuel tank, and hold it with a
suitable bar or block (see Fuel Tank Removal in the Fuel
System (DFI) chapter).
NOTE
When removing the ESD ECU only, there ...
Immobilizer Amplifier Replacement
Remove the upper fairing assembly (see Upper Fairing
Assembly Removal in the Frame chapter).
Disconnect the connector [A].
Pull out the immobilizer amplifier [B] together with the rubber
protector [C] from the air intake duct [D].
ECU Replacement
Refer to the ECU Removal/Instal ...
Radiator Hose and O-ring Replacement
Drain the coolant (see Coolant Change).
Remove:
Upper Fairing Assembly (see Upper Fairing Assembly
Removal in the Frame chapter)
Thermostat Housing [A] (see Thermostat Removal in the
Cooling System chapter)
Oil Cooler [B] (see Oil Cooler Removal in the Engine
Lubrication System chap ...