I'm honestly not sure if TH affects them. They've always been a pain to get to drop; I went on my BST because I didn't feel like changing jobs last time, and went to Grauberg to farm Breeze Geodes. Needed about ten more for my trial so I started farming there since there was a bunch of wind weather (usually is, too!) and it took me a good two hours to get those ten geodes. The T2 Geodes (the -ites) only drop from higher level mobs, and even in an Abyssea party I'm lucky to see more than a handful of them in the pool. Really, as far as I know it's just weather/day that determines which can drop, and I don't think TH has anything to do with it. I haven't tested that, though.