Here's three things I noticed about their pattern:
They react to your movement. If you stand perfectly still, they will stay down.
They will pop up only to attack, which they generally will not do if they don't have a line of sight.
Bombarding them with projectiles while they're down is useless. If you hit them in this state, they will stay down for a couple more seconds.
You want to goad the Host into attacking you so you in turn can hit it.
If it's just one Host, you can align yourself with it and wait for it to pop up. Move back and forth a bit to provoke it if necessary. Shoot it, and dodge its bullets.
If there's several Hosts, you might not want to stand still. Shooting them diagonally while running past is usually the safer option in this case.