This article by Tracy Wilson includes an animation and overview of the popular practice. I recommend Part 1, How Tattoos Work; Part 2 Sterilization; Part 3 Prep Work and Part 5 on Health Risks. The animation illustrates how invasive this procedure is.
We know about the hepatitis risks when tattooing, but there are outbreaks of bacterial infections like M. Chelonae also.
PubMed lists hundreds of cases of adverse reactions to tattooing: lesions, skin cancers on tattoos, diphtheria, dermatitis, rash, psoriasis, itching, abscess, and many other nasty conditions for unlucky tattooees. Rarer effects like penile priapism have been reported.
Art–Do permanent inks belong in a layer of our skin or on paper to decorate say, walls? Only one choice seems harmless. Possible sinfulness aside, perhaps the ancient Jewish prohibition (Lev. 19:28) against tattoos had its roots in the observation that they can subject the skin to disease processes. Was the Torah simply giving its readers/hearers a heads up on avoiding “unclean” lesions rather than taking away a form of self-expression or tribalism?

Oh why did I get that bloody tattoo?
I like your take on Lev: 19:28 yet this is not a sin unto death. These markings were for those who were temple whores and prostitutes. Both male and female. Worshiping the dead-jackasses worship-grove orgy’s-worship etc. The tattoo-paintings-makeup meant certain sexual acts of worship to certain false gods. As we are taught our God is a jealous God. His love for His children gives us free will. He loves us but might hate what we are doing. Indeed study of old testament history is fascinating. I have 1 tattoo…But me and God are still buddies…
I didn’t know that bit of history about temple prostitutes. Unpleasant business, that.