Av8boy
The light was moving on the same side of the moon, i.e. between us and the moon.
It appeared during climb (and cruise) so I do not think that the angle is that super critical.
I am very surprised that this phenomena has not been noticed by many more. One possible reason for this is that the bright light appears slightly below the line of sight when sitting normally in a cockpit seat.
As it appears below and slightly towards the aircraft, perhaps it is missed by so many because, besides the proper angle with the full moon, as well as traveling 'parallel' to the moon, you would have to put your head close to the window to look below to see the light, which only shines occasionally anyway.
I believe it shines occasionally because it must shine on certain surfaces only. Which brings me to another question.......would someone on the ground see the same light?