How long do tattoo waivers take?

Best to just maintain contact with your Recruiter or the Station Commander. Is that the only waiver you are pending? Tattoo waivers can take a bit because of location and albeit a dumb rule, they do need to verify it isn't gang related and that can add some time to it as well. So stay in contact but be patient as best as you can. Don't read anything more into it at this point. Should have no issue getting it approved if that is all the tattoo is.

My arm tattoo goes just at my wrist line and had to get it approved the day I shipped out last minute So I am unsure about the time line for a waiver submitted ahead of time. However, I had an Re code waiver go up the chain really fast and sat at the top for 60 business days until finally approved. It was stressful and annoying but I checked in with my recruiter 3 times a week (which sounds crazy but he appreciated it and had everyone in the office invested) but when I finally just took a breath and stopped obsessing, it was approved. It was 3 months total from when it was initially sent in. Good Luck

How long does ANYTHING in the Army take? Exactly as long as it needs to.

I know that is a horrible answer, but it honestly the most accurate. While there are generalities for every procedure, whether it is promotion, recruitment, retirement, mobilization, or just getting chow, there are also always individual variations. This is doubly true with waivers. Published timelines are (for the most part) guidelines. I wouldn't worry about it unless your recruiter starts worrying about it.