The amount of backlash can be changed by turning the balancer shaft which has eccentric journals.
Start the engine and let it idle.
Loosen the clamp bolt [A] and turn the balancer shaft [B] clockwise [C] until the balancer gear makes a whining sound.
Turn the shaft counterclockwise [D] until the balancer gear whining sound disappears and tighten the clamp bolt.
Torque - Balancer Shaft Clamp Bolt: 9.8 N·m (1.0 kgf·m, 87 in·lb)

Balancer Installation
Balancer Damper InspectionShift Fork/Gear Groove Wear Inspection
Measure the thickness of the shift fork ears [A], and measure
the width [B] of the gear grooves.
If the thickness of a shift fork ear is less than the service
limit, the shift fork must be replaced.
Shift Fork Ear Thickness
Standard: 5.7 6.0 mm (0.224
0.236 in.)
Service Limit: 5.6 mm ...
Exploded View
11. ZX1000JD/KD
AD: Apply adhesive.
AL: Tighten the two clamp bolts alternately two times to ensure even tightening
torque.
G: Apply grease.
L: Apply a non-permanent locking agent.
Specifications
...
Fuel Hose Inspection (fuel leak, damage, installation condition)
If the motorcycle is not properly handled, the high pressure
inside the fuel line can cause fuel to leak [A] or the
hose to burst. Remove the fuel tank (see Fuel Tank Removal
in the Fuel System (DFI) chapter) and check the
fuel hoses.
Replace the fuel hose if any fraying, cracks [B] or ...