I can find documentation saying the Grupo 8 Mirage III EA were based in two locations, Comodoro Rivadavia and Rio Gallegos, both to the south of BA by quite a way. That's not to discount the earlier post saying three were based in BA itself - or your memory Navaleye. I think Rivadavia was actually their C2 node for the FAS so to defend it would make sense.
As far as I can work out there were 17 Mirage III EA originally but 2 were twin seaters. Of the 15 war goers 2 were splashed on day one. (One by Sea Jet the other damaged and then splashed by friendly AAA) So as of May 1 the FAA would be down to 13 total, does anyone have an idea as to their availability rate?
The other tactical consideration is that of OCA sweep when attacking ships. Ships have a MEZ around them, OCA has to sweep around or over the MEZ if it has no SEAD. Medium level sweep into a Sea Dart MEZ would be an incredibly silly idea (as demonstrated later by Learjet). Prior to the landings it made sense to try to attrit Sea Harriers outside the RN MEZ. This wasn't possible for the FAA chaps over San Carlos as their strikers had to penetrate the MEZ to deliver the weapons. Low level sweep through San Carlos would have been incredibly high risk.
The only platform it might have been worth sweeping for would be the Super-E, but that would have given away the element of surprise.
It seems to me that some Mirage III EA were fragged for DCA duties, I wonder if any Argentinian readers could expand on whether this was due to there being no point sweeping for the strikers, Blackbuck, attrition or fuel load?