Received the picture which tells all, or very nearly all!
Wrong, wrong! I've done it again. Not a furniture rack but as you surmised in the first place a Type Rack. Very interesting for me though. This rack, obviously for larger sizes of type, utilizes a rail to hang the 'sorts' on so that the letters thus stored would need to be slotted, widthways, on the underside to allow themselves to be accommodated.
The idea's great for frequently used lines which would justify the permanent occupation of precious bench space but I've not seen it before so I must assume it was not popular here in Australia - I'll probably be trounced for that remark too. A pity the manufacturer's nameplate is obscured at the top/center of the rack, t'would be intersting to know who made 'em.
Thank you for an interesting and illuminating query.