I'm actually surprised to see a topic about the forgotten and hated timmy
Probably the first and the last one, lol. :c
If there's one thing I understood about Mass Effect in general is that "it's either that way" or "it just doesn't make any sort of sense".
Anyway, I thought about this a lot during these years and I agree with most of what you said.
But I believe that the indirect contact he had with the Arca Monolith caused something. The fact that he can speak several alien languages after that proves that his mind was affected somehow. And it's not exactly a good thing when some weird alien thing starts messing around with your brain, now, is it? C:
It's a long way from here to 'indoctrinated' though. In fact, there are two options:
1) This event probably served as the basis for the actual indoctrination process, which went silent, as other people here said, for years and years, maybe fighting TIM's strong will without him even knowing it.
2) No connection with indoctrination. The whole thing was used just to make him aware of a threat against the galaxy and to explain how it led him to create Cerberus (eventually, the reaper larva/reaper tech and cybernetics caused his indoctrination)
The eyes? Just a "cool" feature to make the character even more intimidating and mysterious, in my opinion. There is no explanation behind them, we're talking about mere symbolism.
Following the first option, the Monolith's power to "indoctrinate" was obviously different from what we saw in the games. In Evolution, when Ben touched it, he was transformed into some sort of husk, whose goal was to protect the Monolith at all costs. But, beyond that, he could act normally, he was not a mindless puppet. When he sees Jack (TIM) and Eva, he recognises them and talks to them. That's why I think that this "indoctrination" was less powerful and this makes me think that the indirect contact TIM had was even weaker. I guess that's probably why it took so long to have a significant effect on him.
Someone said that TIM grows more incoherent each time Shep speaks with him, I agree. I started having doubts during their encounter on Thessia, especially what caught my attention is the way he reacts to Shep's words.
(3:47 and 4:01) He sounds defensive and almost disoriented. I remember he was dealing with Aria in Retribution for some business accord about Grayson (lol the meeting was hilarious) and he acted composed and cold when she taunted him. I mean, we all know Aria...if you can handle her, you can handle pretty much anything else. And suddenly he can't handle Shep? Mmh nah. So clearly there was something going on before Thessia. Also, when Kai Leng arrives, the prothean VI detects "indoctrination signs", which means that, shortly after being implanted with cybernetics, he was already affected by them. So, yes, it is possible that TIM started injecting self-replicant nanides in himself even before than expected (but, assuming that the Cerberus videos that Shep watches on Cronos Station, are in chronological order, this doesn't make sense.) Or it just could be that "weak and slow" indoctrination I was talking about in option 1)
And one more thing, about the final scene. There's something about the way he says "I tried, Shepard..." which made me think...Is he referring to that particular moment? Well, because it really doesn't sound like he is. It seems that those words hide a fight which lasted way more than just 5 minutes. So I have two possible explanations:
• First: maybe the reapers started controlling him, or at least they tried, at some point after he implanted himself with cybernetics. (but in this case, if cybernetics are the cause of TIM and Leng's indoctrination, Sanctuary's research was utterly useless and it doesn't make sense again :} ) However, they couldn't do it properly, he somehow understood what was going on but could do nothing about it. He "tried". It was just an internal fight in his head. And Shep repeatedly accusing him of failure, probably brought back his human side for one last moment.
• Second: as I mentioned in the beginning, some things just don't make sense and we have to be okay with it, because the more mysterious and incoherent, the cooler :c
I hope my drunk english was decent enough.
Jesus, how many commas did I use? Almost abusive
Probably the first and the last one, lol. :c 
