A string test at this age will be very accurate. Get a piece of “string”… baling twine is good for this. Put one end of the string on the point of the elbow. Stretch the other end down to the ergot. Then, without moving the end of the string that is held at the elbow, turn the string upwards, up the horse’s side, up past the wither, while holding the same spot on the string that was previously at the ergot. Once it is pointing upwards, where your fingers are holding the twine is the horse’s final height at the wither. Once the growth plates in the leg are at full size, the last growth is in the body, so that is the last part of the horse’s body to mature, and where the late growth is. The legs are at full size earlier. You will see zero, one or two or three inches of string above the wither. Just add this to the horse’s current measured size to get his final height. It’s fairly accurate. The accuracy is dependent on your handling of the string, locating the exact point of the elbow, and holding it in place as you make the turn.
Though the test is the most accurate after the growth plates in the legs are closed, it can be used earlier too, just to get an idea of the mature height. Horse should be at least 18 months old. By then, though the growth plates in the legs are still open and may grow a bit more, most of the growth is there by then with a TB.