Forget the moon phase. I have hunted white tails for nearly 5 decades. Buddy of mine , J. Bush, and I took detailed notes across 3 seasons. I had all of the data once upin a time but tossed it long ago. It was a waste of time and energy. We probably logged 200 days of hunting. We found practically zero correlation between moon phase and deer movement here in the deep south. Only thing that seemed "strong" was that during a full moon and with a clear night sky, they seemed to move later in the day. The number one cause-effect was weather. Cooler weather = more day light movement. N-NW breeze and dropping temps ... good ! E-SE breeze, and warming temps .... not good ! Hour or two after a shower .... good. Driving rain .... bad ! That was about it.
My advice .... just go to the deer woods whenever yo can. Get in the woods early and often, and stay late. And scout....scout...scout.