It's been almost a year, but it varied. One GSTL and one GSA would always carry it with them, but were great about letting people check their breaks. The other GSTL and GSA would leave it at the podium by photo. If I was working photo, I usually helped them stay on track with the break schedule - covering a lane if we were short, or reminding them of the time. Our GE hated having it at the podium, but if he wasn't around, no one cared.
Our GSTLs/GSAs were actually really good about letting people know when their breaks are. I think it's nice when you know when your time is, so you can pace yourself. At least I usually did. 🙂