If you have yet to watch all of Ghost in the Shell, I'd recommend the rest of the franchise;
Movies (Original/Innocence), Stand Alone Complex, and Arise. All three are different interpretations of the same universe.

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Shin Seiki Evangelion and End of Evangelion which is a must watch movie to finish off the TV series
Genocidal Organ - Novel/Manga/Movie (I have only read the book)
All You Need Is Kill (novel/manga) - Manga follows the book to near exact measures so you know the rule, measure and cut once. I wouldn't call it psychological, but it tells of human emotions and survival.

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As for the MAL list... There are non-action psychological gems in there, but if they are not wanted then I second;
Texhnolyze
Ergo Proxy - Small amount of action
Jin-Rou - One of the closest you'll get to GiTS with police and military aspects aside from the Appleseed movies of which I would say were only okay.
PsychoPass - All you need to know is the name, Makishima Shogo-sama
Kara no Kyokai (Movie Series) Good, somewhat psychological, but not cyberpunk
Akira - Classic movie though I didn't think anything particularly special about it. That is a very minority opinion though.

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Some of the above are not exactly cyber-punk. The rest on the list I haven't seen or wouldn't directly recommend.