Gas fireplace inserts are obviously framed in a completely different way from a regular fireplace- it's usually done with wooden studs, plywood and surrounded by air with ducting to carry out the heat. If possible, find plans for the place and look for the detail sheets for the fireplace, cabinets, etc- you would be able to see how the bricks were attached and if there's any kind of gap between the bricks and plywood.

Does this wall have a wooden mantle? If so, look at the rear edge of the top and check for screws (you won't usually find them if it has been painted). If you find them, maybe you could remove it and look at the method for installing the cleat. If it has brackets, you could inspect that, too- even if the bricks were cut to fit around the brackets, you would see some indication of how they were attached to the wall. Worst case, you hunt for studs in the wall, behind the bricks and best case, someone has detailed drawings or photos of the framing.