When the engine is running, the air intake valve is lifting up.
If the valve does not operate properly, check the air intake solenoid valve hoses for leak.
If there are no leaks, check the air intake solenoid valve.

Air Intake Solenoid Valve Unit TestWiring Diagram (US, CA and CAL with KIBS Models)
ZX1000KC
ZX1000KD
...
Overview
S-KTRC is a highly sophisticated system based on MotoGP racing technology.
Unlike the KTRC
system used on the GTR1400 ABS (Concours 14 ABS in N. America), which is
designed to offer rider
reassurance when traversing slippery surfaces, S-KTRC, is designed to maximize
forward motion,
allowing ...
Air Suction Valve Installation
Install the air suction valve so that opening [A] of the reed
faces downward.
Apply a non-permanent locking agent to the threads of
the air suction valve cover bolts [A], and tighten them.
Torque - Air Suction Valve Cover Bolts: 9.8 N·m (1.0 kgf·m,
87 in·lb)
...