That's exactly why we're doing these tests; we are trying to figure out what's happening. I wish Pete had tried the neighboring AF points on his 5DIII. But it's useful info that his 7DII focused on the same spot every time, so there must have been some contrast there (dirt maybe?). I also tried the Tamron 150-600 a couple weeks ago on CPS loan 7DII and there was no issue with the center AF point and bright subjects.
Another easy way to test this is to try to AF on a light bulb that is turned on. Yes, it is bright but still has descent contrast ( the filament, mount, or the actual curves or spiral of a CF bulb) so any of my 5DIII AF points work fine with the Tamron lens, except the center, which half the time has issues. Again, same lens on other bodies, no issue at all. A different lens (400 5.6L, Sigma 120-300 2.8 OS) on the 5DIII, center AF point, no issue. Puzzling. I wonder if it's a metering issue affecting AF, but why only the center point???