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 LubricationOil Pressure Measurement
Remove:
Right Lower Fairing (see Lower Fairing Removal in the
Frame chapter)
Oil Passage Plug [A]
Attach the adapter [A] and gauge [B] to the plug hole.
Special Tools - Oil Pressure Gauge, 10 kgf/cm²: 57001-164
Oil Pressure Gauge Adapter, PT3/8: 57001
-1233
...
Thermostat Installation
Replace the O-rings [A] with new ones, and apply grease
to them.
Assemble:
O-rings
Thermostat Housing [B]
Thermostat [C]
Thermostat Cap [D]
Install the thermostat [A] in the housing so that the air
bleeder hole [B] is on top.
Tighten:
Torque - Thermostat Cap Bolts: 5.9 N ...
Engine Oil
In order for the engine, transmission,
and clutch to function properly, maintain
the engine oil at the proper level,
and change the oil and replace the oil
filter in accordance with the Periodic
Maintenance Chart. Not only do dirt
and metal particles collect in the oil, but
the oil itself los ...