I was about to say that I don't follow your logic here: How would it indicate tailheaviness if a plane doesn't pull itself out of a vertical dive; but I think I understand after pondering for a minute ... you've already trimmed for level flight on the tailheavy plane by introducing down elevator, so now, when you put the plane in the dive, the elevator works to hold it in the dive. Whereas, on a correctly balanced and trimmed plane, the horizontal stab normally adds a downward vector at the rear to counter the CG in front of the center of lift. So, in a vertical dive, where the CG vector lines up with the thrust vector, all you have left are the lift and stab vectors, it will begin to pull itself out of the vertical dive, at least until there is a balancing component of the CG vector to counteract the rotation. Howzzatt?

Phil