So, if you notice the date on this photo it's from 2007. I did this tattoo on my own hand with my own equipment back when I was a professional tattoo artist. I haven't experienced any negative effects from this particular ink, though the tattoo has faded significantly over the years because it has never been touched up, it's nearly 10 years old, and it's on a hand. The problem you run into with talking about tattoo inks and their links to cancer is that literally no tattoo inks are FDA regulated, at all. It's just not a thing they do. Also, doing a bit of digging on the black light inks I'm not seeing any scientific studies done on carcinogenic effects nor am I finding news reports on them. Keep in mind also that there are plenty of standard tattoo pigments that contain various metals that can have adverse reactions in the body (I myself get wicked reactions to anything related to the red colors). Every time you introduce something into the environment within the body you run the risk for allergic reaction or the looming specter of some random reaction that could potentially cause cancer.
It's up to tattoo shops to determine what they want to use on their customers and what they want to have in stock, there ends up being plenty of debate within the industry over what is safe and what is worthwhile. Truth be told I suspect the fact that the ink is more expensive than standard ink, has a shorter shelf life, more limited application and demand and requires far more touch up from the artist to be the more likely grievance (which is a legitimate business reason for not wanting to deal with it at all.) But we're artists not scientists. I haven't seen enough evidence to convince me that there is a particular threat to it, but I'm not going to fault someone for not wanting to take that risk with their customers.
The Yellow King in True Detective is a reference to Chambers' Yellow King from the book/play that drives you insane. I think in the world of True Detective it's meant to be this kind of large cultish cosmic thing that doesn't actually exist but is used as an obsession by some messed up people to do some messed up things.