2) a semicircular block with a handle on top and a blotter on the rounded bottom

I remember those! A desk blotter for use on letters, checks, etc., when we used fountain pens and real ink!
Well, akshully, I still use a Mont Blanc fountain pen that was my Father's... a presentation pen. Great in the hand & never a cramp in fingers when writing with that.
As to the "thing" - from tsuwm's drawing it almost looks like an adjustable desk lamp - if the string was an elecic cord and the bulb was missing.
I give up. You know it's gonna' rattle around in my head - the place where I should have a brain - and drive me nuts!
Thanks? :)