Management tells you when to go. But it’s every other year on your birthday month. So if you don’t get anything you can ask. Your second medical could be as early as 13 months after you first one depending on when you got your first medical and when your birthday is.
The only proof I've ever had that I have a medical was the sheet of paper the flight surgeon handed to me after my exam, which I immediately gave to my sup. Unlike pilots, we don't have to worry about having our medicals on us at all times. I've never received any sort of "official pass" for my ATC medical.