I am making a third attempt at the T2C working smoothly in my Model S. Here is my setup order. It is super specific and weird.
First, make sure your phone's personal hotspot is OFF.
1. Connect the T2C to phone bluetooth through the Phone Settings - Bluetooth
2. Connect the car to the T2C's wifi. The Tesla wifi connection setup (add a wifi network) MUST be done when the car is in forward (not parked). This will allow you to select the new wifi network to "stay on when driving"
3. Now the last step is critical and super wonky. First, you must have already connected the T2C manually through bluetooth for Step 1, NOW you must FORGET the device in the bluetooth setup. It sounds stupid but this sets up the next step which is the key. Leaving the T2C on, now turn on your phone's Personal Hotspot. Now your phone asks to pair a new bluetooth device TO THE HOTSPOT. This is the same T2C device. You pair it right there in the Personal Hotspot page of the phone settings. Lastly, the phone will then ask to allow this device to use CarPlay. Say yes and that is the proper setup. ANYTHING ELSE will not work properly or not at all.
One key distinction I THINK that is happening and that is very hard to understand is that connecting the T2C to the bluetooth as any other bluetooth device (ie through the bluetooth menu on the phone) WILL NOT allow it to access the phone's hotspot. The T2C MUST BE ADDED from the Personal Hotspot phone setting page, THEN it will have access AND show up as a bluetooth device in the phone's bluetooth settings. But again, it MUST BE ADDED at the Personal Hotspot page.
I don't know if this is helpful. I've been pulling my hair out but at least I know how to get it working.
What Carlinkit really needs to do is call the Tesla S3XY Buttons people at
S3XY Buttons by Enhance | Buy Tesla Buttons | Tesla Accessories and setup their T2C to access the car's CanBus system via the S3XY buttons OBD-II hub. Then the Carlinkit can see the status of the car -on/off/drive, etc and become completely reliable and seamless when we get into and leave our vehicles. Once the T2C is setup properly, that is the only thing that is killing the T2C right now - coming and going. It just gets tripped up. They are so close but they need to fix this last piece.