Thanks everyone for your kind comments; Booni, thanks so much for taking the time to analyse that picture.
Somebody sitting with wings half open, to keep cool perhaps, that would make sense. That would also fit with my having seen the same pattern over several minutes.
Certainly I have seen or heard no sign of a second eaglet except for those strange photos. I've been watching a fledgling... Just one. But eagles can be pretty sneaky sometimes, so I wasn't sure what to think.