White light illuminating the engine coming on at intervals in flight; Curious what's the protocol? I was recently flying Air China from Beijing to Bombay &amp; happened to seat on the Window seat close to the wings. 

I could see the engines and there was a light that could illuminate the engines. As I recall it was switched on at some point at the end of taxi and pre takeoff but I don't remember exactly.

What I do remember is that at some points during flight I saw the engine illuminated by this light and at other points (pretty much most of the flight duration) the light was off.

Just curious what the protocol was.

The aircraft type seems to be Airbus A330-300.

https://uk.flightaware.com/live/flight/CCA889

This was a neutral color steady light and not one of the red / blue ones nor the strobe. From the color it looked more like LED illumination. 

PS. From the related question on SE Aviation the responsible light seems to be what they call a "Wing light". But my question is different than that one because why would the flight crew turn on the wing light during cruise altitude flight periodically? 

There was no crew in the cabin for a damage / ice inspection (I've seen them use wing lights for this purpose post a deicing spray but then the flight crew comes into the cabin to look )
The answer is in this post at the very bottom.  In the US these wing lights are usually switched on to make the planes more visible during takeoff and landings despite the fact that the lights are designed for ice inspection.  I don't know if China has the same protocols or not but from what you described it sounds like they do.