Guy Gardener wrote:
Skynet from the future piggybacked inside the Terminatrix into the past where/when she downloaded "it" into the phone systems (She did a dial up gurgle into a payphone, and then everyone is complaining about the phones and computers for the rest for the movie.)
The fact that the TV news station had time to research and prep a segment on a massive computer virus establishes that Skynet has become self-aware and is taking action before the T-X arrives. (Mostow also says in the commentary that they'd intended to show the red leather woman unsuccessfully trying to access an ATM before the T-X got to her, but didn't have time.)
The Badger wrote:
It would make sense to then check the apartment to find out who was killed. Assuming Ginger had some sort of ID, or there were indications that another woman lived at the apartment, the Terminator would continued its mission.
This. And after running out of Sarah Connors in the phone book, it might have had programming to raid a local DMV or police station for more complete records.
It's unknown, moreoever, whether that
Terminator had the ability to scan DNA and a copy of John's info on file to compare it to, as the TX did, but it's entirely plausible it had some good pictures of John, and could estimate the likelihood of any given "Sarah Connor" being the right one based on phenotypic data.