I am sure FBI and TBI know ALL usernames of ET and TC in all electronic venues they use. They are perhaps watching closely. It makes sense if they are also watching closely the potential destinations of any message from the two. They could create new accounts but they have to send to known accounts if they attempt electronic communication.
The one thing I am curious is "would it be possible to monitor burned phones traffics so that LE know which burned phones are excessively watching the news about ET's amber alert?" I am 99.99% sure TC watches the news about the Amber Alert. If he cannot go to restaurants and other public places to watch TV, he has a TV where he is hidden and/or he has phone or tablet able to go to the Internet. IMO.
I'm a paralegal and subpoena cell phone records all of the time. Burner phone information is non existent unless they registered their phone to pay for minutes online. Also, the cell phone carriers track data usage but not specific websites visited. That's what concerns me about a AirBnB rental. Book one on a phone and there isn't a way to track that if not paid with a personal credit card. I hope that FBI has more tools.