The water runs along the walls/leaves and drops to the ground, which is (for now) a layer of peat of 1,2 cm, a layer of white filtration thing of 0.5 cm and about 10 cm of blue filtration foam. Water is only about 5 cm deep where there's nothing.If you have a way for the excess water to drain from the tank, constant water might work while the plants are establishing; I'd watch the bases of the bromelids for rot, but other than that it shouldn't be a problem. Of course I can't guarantee that. Once the plants are established, you only need to do enough to keep the humidity where it needs to be and to keep animals and plants hydrated; which could be 4on/4off, or even on an hour in the morning and again in the evening. It'll take some tweaking.
There's no dry spot in the entire thing, apart from a piece of wood and the windows.
Rain, though, is constant right now.
Lemme try to make a short video so you get an idea.

I actually meant full, not empty! xDThe axils of the bromeliads can have water in them, infact this is why some people use them to breed certain dartfrog species. Not all broms naturally hold water though, and the water generally drains immediately in those that don't. Infact, water in the crowns of bromeliads could act as water sources for the geckos.
I believe only one of my broms has an empty tank.
I tried a few other plants, including a dwarf orchid, but since the store couldn't get the latin name, I don't know if it'll work. I don't even know if it's epiphyte...