Does anybody have any advice, on or examples of, a Motion for Rehearing under TRAP 49 they can share? There's a issue that we'd like the 11th CoA to take one more look at in a case, but I've never asked for a rehearing and am a little uncertain of what the form and content should be.

check out the State's Appellate Manual. There is a chapter on motions for rehearing that has some examples. Key points to remember are maintining a respectful tone and concentrating on issues the Court can fix, IMO. It is hard to say "you are wrong" in a nice way, but that is what you need to do. What I look for in a rehearing is facts they overlooked in the record and other, controlling statutes or cases that their opinion violates. There are other errors, of course, but those seem to me the best type to fix this way.

Thanks, I'll do that. Thanks to the response I got via email as well.