Actually the ones concerning mental illness take this into account in great detail. Have you read any of them? They are easy to find.
Yes, I have read some, the only ones which make mention of exposure to light are ones that only talk about it during full moon phase. It is therefore impossible to seperate any effects of light from the effects of phase, leaving my assertion that there are no well documented studies showing the harmfulness of moonlight intact.
Unless you have found one which does make this separation? If so, please link it.
I would also think it obvious to sensible readers that the time of greatest exposure to moonlight is not during full moon at all but at another time of the moons phase, but Im sure being such an expert you already know this.