Well, I'm dealing with this today.
Had the same 12:30 - 2:30 window and waited until 3:30 before trying to figure out what was going on.
1) Replied to the text confirmation they sent me yesterday but I don't think that number receives messages;
2) Checked the app for some way to see status and/or request updates but no such capabilities;
3) Checked the website for the same but, again, no such options;
4) Called the main number but the menu system did nothing but direct me to the chat option on the website;
5) Looked for the chat option on the website but no luck so sent a "message" (no appropriate subject in drop down);
6) Called main number again and used check on service status option which forwarded me to one of the Service Centers;
7) After that guy said Mobile Techs are dispatched from a different SC (he tried to help), I said I'd try calling that SC;
8) Called the dispatch SC but system put me back into the main phone queue;
9) Called that SC's sales department but got the too busy announcement;
10) Sales person called me back (saw my caller ID) and put my info in front of the dispatcher to call me back in 5 minutes;
11) Withing 5 minutes (4:07pm), got a call from an unknown number which turned out to be the Mobile Tech stuck in traffic and on his way with an ETA of 20 minutes (more like 40 from his location). He said that he'd been trying to get to me for an hour (30 minutes after the original window) and said that he needs to talk to the higher ups about how long the windows are and how many appointments are in each window - said I should've been in the late afternoon window instead of the early afternoon one.
Never got a call back from the dispatcher so, either he prompted the tech to call me or he forgot/never really knew he was supposed to.
Basically, as we all know, communication is a huge issue at Tesla and they could save themselves a lot of work by truly making our ability to find out what's going on, independently, a lot easier. I can track the progress of my pizza but I can't figure out when the Mobile Tech might actually be making it to my location. Before you know it, Tesla will be used by comedians in lieu of the cable guy.