I'm sure Tracy has already read this study in the past, but not everyone has. Not so much on cats, but it's a very interesting study done on the coyote. It was looking at coyote response for certain scents as are outlined, but they also mention the lunar cycle.
They found no statistical evidence of lunar cycle affecting the overall attraction of lures for coyotes, but they did mention something quite significant in there if you can find it. Although no difference was found in lure attraction they did find that there was a trend in relation to barometric pressure and coyote captures.
I've been perplexed in the past as I see temperatures dropping, and expecting large catches the next morning as the change in temperature I assumed would get animals moving. I'm usually humbled as nights in the past I thought would be great were duds, and other nights I didn't plan on much I was filled up.
This was the first year after really reading through the study carefully I began to watch barometric pressure readings. I pretty much quit watching the temperatures, and only noted large dips or increases in barometric pressure.
Just as Major Boddicker over 30 years ago noted it's amazing with even just a point or two change on the barometric pressure the animal activity increases greatly. If it remains relatively stable for a few days the animal movement is average at best. I have no answer for how, but these animals will change behavior based on the barometric pressure. I've found it is more of a predictor of animal movement then the lunar cycle for myself.
https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1066&context=gpwdcwp