One thing I do know for sure about barometric pressure is I've caught some of my best fish right before a big storm hits when the winds pick up, the sky is black and the lightning if flashing on the horizon.
As for the moon phases, I don't wait for a full moon to go fishing, but I find it does definitely improve the fishing when it does happen.
Couple years back I was on my annual trip to the West Arm of Nippissing with a full moon forecast in the coming days, and one day in particular had the full moon rising at the exact time as the sun was setting and I planned to be on a favorite spot when it happened.
Couple days before the event and shortly before sunset I caught this fish.
Day before the event and again near sunset I got this one.
The day of the event and just about 15 minutes before the exact moonrise/sunset time I hooked and lost a big fish near the boat. I continued on and was on my spot and exactly as I watched the full moon rise & the sun set at the same time this 50"er hit right on cue.
Certainly not the 1st time I've seen this happen and hopefully not the last, but in my opinion I think moon phases definitely trigger fish.
I'll be back up there again in a few weeks and again there's gonna be a full moon, so we'll see what happens.