The original Skynet estimated Sarah Connor to be in LA around 1984.
Policeman: Why were the other women killed?
Reese: Records were lost in the war.
Skynet knew almost nothing about Connor's mother.
Her full name, where she lived. They just knew the city.
The Terminator was just being systematic.
The second Terminator, coming through from the altered timeline probably didn't know where Sarah Connor was for the first terminator. They knew that at some point Cyberdyne Systems appropriated the first Terminator's remains. By then Sarah Connor had skipped to Mexico and disappeared.
It wasn't until Sarah Connor was in the mental institution and John Connor was in foster care that the new Skynet was able to locate records of their whereabouts.
I suppose you could send a Terminator back and let it wander around for 12 years hoping that it bumps into Sarah Connor. But really you send it back to when you have confirmed where she is, the mental institution in 1992.