I've run across this too. It would seem that the sim only allows a certain number of one type of sprite at a time. Sprites are the particles that are emitted by effects files, like those that are responsible for making lights look, well, bright.

How comfortable would you be with opening and maybe editing those lighting effects?

The reason being, I've found that many effects used for lighting, have an entry in them that spcifies that effect as a light source. Meaning there is the light "bulb", if you will, and a seperate light "glow", that makes the "bulb" appear to light up the model around it.  The glow is what seems to cause the problem. With many (most, in fact) vclighing effects, the glow is all there is. When too many of these glow effects are assigned to be on at once, some won't show up.

I THINK this is why your cockpit lights are flashing. I suspect the wing strobes or nav lights (or both) are using this glow effect, and when they flash, it's just too many for the sim to render, thus killing the cockpit lights for a moment.

If you feel comfortable editing effects, I can talk you through the process of fixing this issue. (Of course, you could also eliminate a few of the light entries from the aircraft.cfg, but where's the fun in that?)

It's not a tutorial as such, but you might look into the the FS9 special effects SDK. I've found it invaluable.