If the oil leakage is found on it, replace the steering damper with a new one (see Steering Damper Removal/ Installation in the Steering chapter).

ZX1000JD/KD [B]

Steering Stem Bearing LubricationGear Position Switch Output Voltage Inspection
NOTE
Be sure the battery is fully charged.
Turn the ignition switch to OFF.
Remove the fuel tank (see Fuel Tank Removal in the Fuel
System (DFI) chapter).
Disconnect the sidestand switch/gear position switch lead
connector [A].
Connect the measuring adapter [A] between the ...
Lights and Switches Operation Inspection
First Step
Set the gear position in the neutral position.
Turn the ignition switch to ON.
The following lights should go on according to below table.
If the following light does not go on, inspect the meter
unit (see Meter Unit Inspection in the Electrical System
chapter).
...
Additional Considerations for High Speed Operation
Brakes: The importance of the brakes, especially during high speed
operation,
cannot be overemphasized. Check to see that they are correctly adjusted and
functioning
properly.
Steering: Looseness in the steering can cause loss of control. Check to see that
the handlebar turns freely but ha ...