Whenever I’ve gotten a tattoo or piercing I’ve had to fill out a consent form stating I’ve recently eaten/drank something (as well as all the other stuff like if I’ve had alcohol, any medical conditions etc.) personally wouldn’t risk it though :)
I have gotten a tattoo (6-7 hour session) while on a short fast (It was only 36 hours or so IIRC) with no issues. I see no reason why fasting should affect things, but I cannot say for certain.
HOWEVER, I am in the camp of why risk it? None of us here can likely give you solid empirical evidence to say one way or the other. But we do know that NOT being fasted works for getting tattoos. So if you are a little unsure, I would just break your fast for the tattoo and give it a week of healing time before getting back in to prolonged fasts.