unless you get a high pressure pump, or tie-in to your mains supply directly, you’ll have a hard time creating enough pressure to mist. The best thing, short of a mistking (or similar), is to use a garden hose timer, plumbed into a faucet, and a set of patio misting nozzles. While this can certainly be done, I am less than optimistic that the time, effort and cost involved will prove worthwhile compared to buying a mist-king. The difficulties are several: You are going to need to generate at least 35psi to run even the coarsest misting nozzle. Most mains supplies will deliver this, but you’ll need an indoor tap to hook up to, and a garden hose timer. So you’ll either need to do some plumbing,move your enclosure close to an indoor tap, or else run garden hose to your cage. (I wouldn’t advise the latter). I’m not trying to dissuade your ingenuity, I’m just suggesting that, for an indoor cage, it might be better to devote your diy creativity to some other aspect of husbandry.