Based on these excellent questions it appears that writing with ink permanently on the skin is forbidden and that there is no question of maras ayin for non permanent tattoos. Is there a way to make a permanent image on the skin that does not violate halacha?
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This answer states that permanent makeup is allowed. He bases it mainly on the fact tattooing is forbidden when two actions are involved - writing (ink filling) and scratching/cutting into the skin.
However, he adds a few more things into the discussion, one is that the outcome is just some color, not a distinguishable shape. Another - that it's not really permanent but eventually wears off. Both of these don't seem to fit in with what you're asking.
Rabbi Yaakov Ariel says that in his opinion even a temporary tattoo is forbidden, this would seem to be the same here.
I argue here based on the Gemara (Makos 21a), the Shulchan Aruch (YD § 180), and other sources, that when (1) a particular tattoo is in fact non-idolatrous; and (2) the very nature of the particular tattoo is such that it can be objectively presumed to be non-idolatrous, it is permissible under normative halacha.
This applies, for example, to permanent makeup, which is non-idolatrous, and the very nature of the tattoo is beautification and can therefore be objectively presumed to be non-idolatrous.