The medicine cabinets were installed on the wall in the standard way, with two large bolts in each upper corner, plus big screw anchors for good measure. The crafty DIY-er who was here before me added an L bracket to the bottom for good measure. I simply unscrewed all the bolts, and the cabinets easily came down (they were kind of heavy though, and I probably could have benefitted from a helper).
One cabinet down:
Both cabinets down:
I knew I was going to find some sort of hole in the wall (I assumed from a former small, recessed medicine cabinet), but I wasn't sure what form it would take. Many different approaches had been used over the years to cover up this hole, from a gypsum-board-and-skim-coat-of-plaster patch to these small fiber boards, almost like artist panels for painting, lightly tacked up with finishing nails.
Fiber board panels removed:
After removing the small panels, I found interesting evidence of the Ear's history and construction.
A scrap of fancy old wallpaper, with a shiny black finish and shiny gold accents:
Many different surfaces and materials, from gypsum board to plaster and lathe: