The active engine mount is effective during idling under engine speed of 900 RPM.
Signals that are synchronized to the engine RPM are sent by the ECM to the VSV, and engine vacuum is thereby utilized to vary the pressure of the intake air chamber in the active control engine mount. As a result, the diaphragm vibrates, and using the liquid as a medium, the rubber mount also vibrates. This vibration of the engine mount acts to cancel out the engine vibration during idle, thus reducing vibration and noise at idle. The active engine mount’s damping force to generate vibrations is calibrated through the effects of the orifice and the vacuum side branch.
View attachment 300638
The only vacuum problem that could conceivably affect braking is a vacuum leak that depletes the vacuum stored in the vacuum buffer canister for use when brakes are applied while engine vacuum is low. But even this would not cause the steering wheel to shake from side-to-side during braking.
Did you have too remove a wheel and tire for any reason during, or just before or after, the spark plug change?