You keep citing the artist's age and bashing millennials, all while ignoring your behavior that you've so kindly spelled out for us. If you've been hanging out in tattoo shops for 20 years now, you should know that some days can be very hectic/non-stop/chaotic. You should also know that days like that can leave an artist with little to no opportunities to take a breather. I know that personally, the last thing I'm doing when I get a quick breather during a busy day is CHECKING MY EMAIL. If you are so hellbent on getting a tattoo, pick up a telephone or get into your car and go to the shop, make your intentions known, and get a tattoo. Face-to-face communication still reigns supreme in this industry. It lets artists know that you're not wasting their time.
I think you've gotten some pretty good advice and perspective from the other responses in this thread. If he's a good kid and does good work (which you've implied he does), go to the shop IN-PERSON, schedule a time to get the tattoo, and if you really feel the need, as him what the best way to schedule your next appointment with him will be, as you didn't feel you got a clear response from him the last time around. There's value in being diplomatic, and you might be able to teach the kid a lesson on professionalism without coming off like an asshole.