OK, I kept searching, and with a Google search criterion of:
site:luminous-landscape.com macbeth "color checker" "second patch"
... the thread I was thinking about came up as the first hit:
http://luminous-landscape.com/forum/lofive...php/t18026.html(Shows yet again that a Google site-targeted search often is vastly superior to the target site's own search engine; in my case, LL's kept coming up nil.)
So now I'm able to answer my own questions:
The deleterious consequence of using the near-specular white patch is running the risk of clipping channels, leading to an inaccurate adjustment; the second grayer patch gives one some headroom, but still is light enough to take a proper white balance reading.
Nevertheless, yesterday I was able to play around with my friend's GL2 white balance adjustment, and I must say that despite pointing it a number of very white specular surfaces (completely filling the view, of course), the color balance always came out well on-screen, visually at least. (Perhaps I'm coining a phrase: "pleasing white balance"? Heh!)
On the other hand, looking at the transmissive light source of the screen shining light directly into my eyes, maybe I was being fooled by the perceptual phenomenon of chromatic adaptation, neutralizing any slight casts from the aforementioned possible inaccurate adjustments due to channel clipping, whereas such casts may stick out like a sore thumb were the capture to go to print, where I'd be looking at reflective light without the "protection" of cast-neutralizing chromatic adaptation.
So I guess the practical danger of not using the second patch really depends on whether the final viewing will be on screen or on printed material.