Eversharp pencils like these show up on page 78 of The Catalogue, in frame 48 ("Eversharp in Decline"):
The pens have an interesting mechanism – the button on the top advances the tip, while the button that sticks out of the clip, when pressed, releases it:
Matt McColm, being the keen observer that he is, read my Baltimore show report and sent me an email asking me what on earth a pencil collector was doing picking up a bunch of "Small Ball" pens.
"Small ball?" I asked. I’d never heard them called by name before – the 1953 repair manual refers to them only as "ballpoint pens" and "propel-repel" pencils. So Matt sent me a link to an advertisement offered by an online seller, and sure enough he’s right. I couldn’t get permission to use that photograph (the seller wanted to sell me the ad instead, for what I thought was waaay too much), but thanks to Google Books (again), I did track down another ad that appeared in the November 29, 1954 issue of "The Deseret News and Salt Lake Telegram":
The ball on these pens was smaller than the ballpoints Eversharp had been producing prior to the introduction of these pens, but comparable in size to the Parker Jotters and the hundreds of other ballpoints that followed. It was an innovation by Eversharp standards, but in retrospect, it was a dying company simply catching up to what everyone else was already doing.
If this set is complete and correct, it looks like the Small Ball either remained in production or leftover stock was sold after Parker acquired Eversharp’s writing division in 1957:
Matt wasn’t finished with me on these. Armed with the knowledge that I was a sucker for an Eversharp ballpoint, a couple weeks later he sent me a link to another auction, with the comment that there should be a matching pencil for this one:
I agree. There should be a matching pencil. The hunt is on!