After extensive study of the Qunari specimens you kindly provided, I’ve come to the conclusion that the painted markings on their face and body are not, in fact, solely for ceremonial purpose, but provide a practical benefit. Oh, I’m certain there is some cultural significance to the patterns and colors they choose, but the Qunari do nothing without purpose, yes?
They call these markings “vitaar,” which in their tongue means “poison armor.” It’s called this because the markings are magical in nature and actually harden their skin to an iron-like quality without hindering flexibility, and my analysis says the paint consists largely of poison. It’s mixed with something else—blood, perhaps their own?—and that neutralizes the poison, but only for one with Qunari physiology. Anyone else would perish almost instantly (which reminds me: I’ll kindly require another body slave). The process activates the magical qualities of the poison, which provides the protective effects, almost in the same manner that lyrium runes do.
How this works, and whether it can be used for our purposes, will require further study. Perhaps some live specimens this time?
What you see are vitaar, not tattoos. I’m not sure anyone who’s worked on creating the games has explained why he has his vitaar “armor” on for the sex scenes. (There are some fan theories about Bull not wanting to be completely vulnerable–emotionally or physically?) But. From reading the above, it sounds like they would not poison a non-Qunari partner because it’s not actually poison once it is applied to the body. It goes into effect of hardening the skin and creating a magical protection effect.
Now if you want to say he has tattoos in your own headcannon, that’s totally valid. But if you’re confused about how his markings come and go: they’re not tattoos, they are vitaar.