After replacing the display assembly, the effect is no longer present.
I think this is officially another in the long list of "random issues caused by Apple's terrible ribbon cables". While this effect is new to me, the fact that Apple uses ribbon cables that are too short on some of their models, leading to stresses that cause unpredictable problems is not. Rather sad for a "premium" product, but it is what it is.
Replacing the display assembly was the solution. And examining the ribbon cables under my microscope did show what looked like small stresses on the ribbon cable at the point it attaches to the screen. Documenting this here for posterity so if someone else in the future encounters this strange phenomena, they'll be able to find an answer and solution.