I have what is probably the same issue, pictured below - perhaps all or most cages do this. I believe it's just water running down the beam, then collecting in the gutter attachment area, then dripping - in my case usually for about an hour after it rains. For me it's just mildly annoying and never rose to the level of trying to fix it. Agreeing with
@ajw22 that a bead of silicone on the front and rear of that lower bracket might solve it. But I never did that b/c I thought perhaps it would just trap the water inside, which I thought can't be a good thing long term. And who knows, maybe it would just "fill up" that area of the beam until it overflows and drips again. Worth a try perhaps. Like yours, the area is prone to algae buildup and I just hit it with powerwashing twice a year - or the chlorine mixture I use to clean the cage more easily. Off topic from the OP, but my screen guy tries to convince me not to use chlorine since it rusts the screws, especially at the base. But it's so much easier than pressure washing and the chlorine splashes above to clean the top too, which deters new algae from forming. Fyi I uses a 50/50 mix of pool store chlorine (11%) and water, which is basically resulting like the 5% store bleach. Yes, I replace rusted screws at the base from time to time. Better rinsing would help

Love the look of the pine trees, hate the needles. I found a new way to clean them from the gutter adjacent to the pool cage without crawling down the roof. I take my telescoping tree saw complete with blade, hang a towel on the blade, extend it out over the gutter as far out as possible while standing on a ladder to the side of the cage/gutter. Turn the saw to drop the towel into the gutter. Pull the saw out and thread it back in the gutter under gutter straps and when you reach to towel, turn the saw to grab the towel then withdraw it with all the needles grabbed. Fun that, and it prevents my wife from agonizing about me crawling around the tile roof! Good luck, ideas welcome.
