I would love to know more about that last sentence if anyone has any resources.
According to the NY Times, this ban wasn't exactly enforced:
So, why did it take 36 years to lift the ban? What was the impetus that finally got it accomplished in 1997?
I'm really sorry I missed it, but they New York historical society recently had an exhibit about tattooing in New York. Especially addressing some of the culture around tattoos during this period.
http://www.nyhistory.org/exhibitions/tattooed-new-york#
As the article you linked mentions. The stated reason was a hepatitis outbreak in the 60's. I think the impetus for repeal was just getting it back out into the open so that it would be safer and not making criminals out of the thousands of artists and customers of tattoo parlors. It was pretty out in the open by that time and the Health department had no concerns.