EEG?
EEG is easier to administer, but the PET scan gives very detailed information, and would identify -- with particularity and specificity -- cortical areas, i.e., in the frontal lobe, when she is responding, and in the language-generating areas of the left temporal lobe, when she is attempting to speak. (**BTW, I have a degree in Neuroscience as well as a Law degree**)
In other words, it would say a lot, and put to rest a lot of the speculation regarding "brain-stem only" avtivity.
But if Judge Greer arranges for her to die now, he'll never be subject to being second-guessed. And that is what's driving his inexplicable decision-making.