I'm confused--are you saying the T-800 in T1 showing emotion was intentional, and appropriate for the character because it would have been an automatic physiological response? I don't think the films suggest one way or the other whether or not this is true. But saying T1 T-800 showed too much emotion, or T2 T-800 didn't show enough, would be a nitpick IMO because in general both showed very little, obviously by design. The clear intention in the film was that both were supposed to be the same model of Terminator, that would behave in a similar way in similar situations with similar instructions.
i don't know about intentions. i know that "survelliance camera" effect, i.e. inhuman face, was intentional.
at the same time i know that:
- endoskull holes for human nerves were intentional (just because they were there and exactly at correct places)
- without additional hardware a terminator cannot move its meat face, and there was no metal hardware there - so they should be live nerves connected to the CPU
- a terminator must be an infiltrator, and that means its programming should have some emotions emulator, presumably generated outside its main programming or just lamely programmed
- a doll had its flesh moving for no reason in a close-up like if cut nerves caused some trouble in mimics
so a live actor terminator has a poker face when it doesn't do anything, but it changes that face often - angry face in the police car or when killing its police driver before, disgust when returning from first failed purchase, crazy face while crazy shooting UZI.
does it have hardware and software for that? yes it does.
was it intentional? i cannot say "it wasn't" taking into concideration all above.
as for T2, it was dumber than T1 before some event that will be named later.
T1 easily learned the meaning of swearing and at the same time could easily provide some random mother-daughter dialogue with Sarah. that demands ability to analyse behaviour+speech at the same time + learning to use them itself.
T2 was so dumb at copying humans that John had to teach him and in directors cut (which i take as the proper version) to change its chip programming conditions. and - voila - after that he started not just to understand humans but to show emotions, and i'm not talking about smiling only: something like tiredness and self-anger for its own disability against T-1000 can be easily seen. or remember sending Jonh&Sarah away and its face while shouting and later while searching for T-1000. it's totally not what it was in WHY CANNOT I KILL HUMANS scene.
so no, T1 and T2 behaved very differently before "switching to write mode", presumably to difference in programming (lack it in case of T2): Skynet surely could prepare its own infiltrator better than humans, T1 got more programming or had his "switch" "on" from the beginning.
both didn't have a poker face during their missions, one needed a kick to start that programming, another had it from the beginning.