I'll admit that I didn't click on the puzzle piece, which may point to a shortcoming to how it messages to the user (its tooltip says "Extensions", maybe "All enabled extensions" might have made me try it.) It sure would have helped if disabling extensions, which removes their icon from the list, would also have surfaced the icon for the one that I just added, but it doesn't. One can understand that chromium would limit the number of icons shown at any given time and provide the puzzle piece to support overflow, but if disabling extensions removes their icon, it should really be the case that if other extensions are available, then one of them should be selected to replace the disabled extension. As it is the UX only provides only half of the feedback a reasonable user might expect as he's enabling/disabling. I note that if the icon for an extension was showing, and you disable the extension, the icon disappear, and if you enable it it re-appears, but not so for the one that I just added.
Finally: I surmised that if I quit chrome, and restarted it, then the new set of icons (only those enabled) would show up. But no, that doesn't work either. So there appear to be a pre-approved set of extension for which the icon shows, and the rest only shows in the overflow popup. And if, after restarting chrome, I re-enable the extensions that did show when enabled but do not show since I disable them, then they re-appear. So they're special in some way. After restarting chrome, with some extensions disabled, the print this page extension still only shows in the overflow popup:

I then re-enable some extensions, they are promoted to outside of the overflow: