Been tracking this for years actually and yes, there does seem to be a pattern. From what I've logged in my own case files, new moon and full moon both seem to produce upticks in missing time reports but for different reasons possibly. Full moon cases tend to involve more witnesses, new moon cases tend to be solo and the experiencers are often more confused about what happened.
I've got maybe 40 documented cases I've collected over the past decade or so and when I plotted them against a lunar calendar the correlation wasn't perfect but it was noticeable enough that I couldn't dismiss it. Someone else here done the same thing? Would be interesting to compare data properly rather than just trading anecdotes.
The cynics will say people are just more likely to be outside during a full moon so obviously you get more sightings. That's fair up to a point but it doesn't explain the new moon clustering at all. Has anyone noticed whether the duration of the missing time varies between phases too? That's the bit I cant figure out.