It's a shame G0-T0 is so terrible in gameplay that nobody wants to use him, because he's a fascinating character who fits in well with KotOR II's overarching story. Goto might be the most intelligent, influential, and independent droid character in Star Wars. We don't know what Goto was like back when he was a bright-eyed little circuit board fresh off the assembly line, other than he had a very tinny voice, but since he intentionally built his new demeanor around fictional mob boss clichés it's safe to say he was a very different droid. Now he's gone completely rogue, but unlike violent droids rebelling against their masters, Goto built up a criminal enterprise with the intent of safeguarding galactic civilization.
Unlike Kreia, whose endgame could be one of several incompatible options depending on who you ask, Goto has a clearly defined objective all his schemes work towards: help the Republic stabilize and recover in the wake of multiple devastating wars. That's what he was designed and built to do, but he couldn't, because the magnitude of the problem was beyond his ability to solve. In order to get anywhere close, he had to break the rules he was programmed to follow and completely alter himself in the process, taking on the guise of someone capable of doing what his earlier self couldn't.
All this together makes Goto, depending on how you play the game, the character most similar to the Exile. Both were given demands which were impossible for them to meet, contradictions of everything about them which left them damaged and forced to make compromises. Their compromises made them flawed in the eyes of the people making demands, leaving them to deal with everything alone.
Goto doesn't show much emotion other than constant annoyance, but when describing his breakdown he sounds almost saddened, referring to his past self as "the droid" like he doesn't want to acknowledge his inability to perform his function.
That dissociation isn't part of masking his identity, at this point in the dialogue the jig is up. He only considers himself to be that broken droid when he’s making the correct decision because there is no room for failure so anything that is wrong must not be him.
Now he keeps trying to fulfill his objectives because he's still programmed to do it, but the way he explains it sounds more like an obligation than a programmed function. With what happens in the game it's easy to play the Exile with similar feelings, being another independent actor trying to save the Jedi and the Republic because it's the best available option despite the obstinance and criticism from people they are trying to help.
