This should not be confused with Ghost in the Shell which is a media franchise, though I named this theme after it.

This theme is very similar to, and possibly a sub-theme of, the Do Androids Dream of Electric Sheep? theme. Though the difference is subtle, there is a big difference.
Do Android Dream of Electric Sheep? is focused on the ambiguity of consciousness in artificial intelligence, while this theme isn’t really focused on the ambiguity of it at all.

Ghost in the Shell is really best pictured via this quote from I, Robot (the film):

There have always been ghosts in the machine. Random segments of code, that have grouped together to form unexpected protocols. Unanticipated, these free radicals engender questions of free will, creativity, and even the nature of what we might call the soul. Why is it that when some robots are left in darkness, they will seek out the light?

But to elaborate on that…what it means is that the artificial intelligence starts doing things that it was never really intended to do…and doing so in a way that is suspiciously close to consciousness.
This is, usually, because artificial intelligence possessing consciousness is somewhat confirmed or, at the very least, strongly hinted at.

Though this theme can and often does overlap with Do Androids Dream of Electric Sheep?. That theme is mostly focused on whether artificial intelligence can possess a soul, while this one is focused on whether or not it’s already there.

The exploration of this theme is less focused on existential questions and more like:

• Why do robots in the dark seem to go towards the light? (I, Robot)
• Why do robots tend to huddle together? (I, Robot)
• Is the artificial intelligence expressing love?

I’ll come up with more questions gradually.

I will be honest: I’m questioning whether this is me splitting hairs for no reason or not.

Could be argued to be an example of Ghost in the Shell, though it suffers from the same issue as I, Robot…though worse, somehow.

This film doesn’t actually explore it, because it presumes that David is self-aware and clearly demonstrates that all androids in the film have consciousness.

The one thing that might trip a viewer up is that one of the characters states, explicitly, that David was acting strangely. But that doesn’t mean it’s an example of this theme: because the character points out something that isn’t obvious to him, but is obvious to us.

From what I gathered, although this is where the name of the theme comes from…there is only really one proper example of this in the entire series: Episode 3 of Stand Alone Complex: ささやかな反乱 / ANDROID AND I.
This is because that episode is about a guy who falls in love with his sex bot, goes crazy and then intends to destroy every other android of that model so that his one remains the only one. It’s stated that this specific model is quite limited and outdated, but it’s still liked. This is shown with the android repeating certain phrases from movies or whatever the owner said. At the end, Togusa hears the android repeat a quote from a film which he dismisses at first. But when he comes home, the film it’s from just happens to be playing…and he hears the full quote. And it’s different.
The quote from the film is:

No, I suppose I am crazy. I don’t want to be in love with you anymore.

The android’s quote:

No, I suppose I am crazy. I don’t want to go with you. I don’t want to be in love with you anymore. I’m sorry, I really did love you

It’s also notable that the members of Section 9 are a little confused by the android’s actions.

Though an ambiguous example would be Solid State Society. Regarding the antagonist, who is a ‘shard’ of Kusanagi, whatever the Hell that means.
It’s ambiguous because this shard obviously thinks logically and has Kusanagi’s moral compass…but it’s actually super ambiguous whether this is an AI or not and whether it’s even conscious or not. Is it an example of Do Androids Dream of Electric Sheep? M-maybe…

The 2004 film with Will Smith. Yes, really.

This film actually takes this theme more seriously than the other theme (Do Androids Dream of Electric Sheep?)…and, well, that should be evident from the fact that I used a quote from the film to illustrate this theme.

However, exploration is also a bit dubious because, well, they kinda spell it out and show it directly. The film would be far better at communicating this if it wasn’t pointed out and were more subtle: IE, the protagonist sees robots expressing strange behavior which is neither logical nor malicious, which would hint at this.