Bounding Box in Classifications might not be possible (btw, can any Solibrian tell us why?) but what about bottom area? I guess the vertical bars have just a very small one and this might help you to distinguish them via classification settings if there is no property or special naming which could help you here.
Another possibility might be to use nested rules as there is indeed the possibility to check for Bounding Box Values. So then I would suggest you to go for two hierarchies, one for the Vertical bars and another one for the Horizontal ones. Both of them would contain the same subrule which is either #222 or #234 and only checks the passed components of the main rule.
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Although I do not really understand why you have to know first if it is vertical or horizontal for checking as you can also define in the rules which dimension (x/y or z) the min and max spacing should be. If it just for classification ok, but actually it should not limitate you can filter them out in ITOs as well using the same method - there you can tick the bounding box values as we know.
Also do you know how to edit multiple rows of an ITO manually? => You mean changing the classification manually there based on what you see? You could try to preserve the order and match the ITO with the classification table e.g. with the GUID. Then export both excel and fix it there with copy paste. When done, import it again. However, this might be not the smartest way, or even a bit adventurous, but should work too.