Asperger's comes to mind. High functioning Asperger people (like myself) can be very intelligent (Sheldon on Big Bang Theory). Sometimes we hide it very well.
The best explanation I have found is, "Whilst adults with autism and Asperger Syndrome are able to detect basic mental states in the whole face, they are impaired at recognizing complex mental states, and are markedly impaired at recognizing such mental states from the eyes alone."
We are bad at reading body language, and see no information in other people's eyes, hence we tend to look at their mouth when talking with them, since that's where the information comes from (for us at least). Tend to be socially awkward. Though we try.
Great benefits of dating an aspie is we are very honest, loyal, have deep feelings despite not showing them in conventional ways (I've been told I have a "poker face".) I was afraid I might not be able to be a good husband to my wife. She replied, "I'm the luckiest woman alive."
Some aspies have difficulty looking other people "in the eye". They say it burns. I just see eyes, and I've been trained to look there because that's what other people expect. (Or we just learn it along the way.) But don't look too long. Look for 5 seconds, look away for 2 seconds, look back for 5 seconds, repeat. Soon I either forget what the conversation is because I'm spending my time counting seconds, or I forget to do it because I'm busy having a conversation, in which case I probably don't look them in the eye as much as I should, as I find it distracting.
Unclear if that's what your friend has. Just what came to mind as a possibility.
One thing I'd like to ask is that when he does the laugh and then uses a different voice, is he in the same moment he was prior? It is hard to remember what happened to another personality when one switches. Noticing this? He could also be neurodivergent and developed this as a coping mechanism. Not really switching personalities but changing tone and trying to maintain self control.
Also, I should add, my grandma used to change her voice when she was trying to be funny or lighten the mood. Like, say in a normal voice, "I've got work to do," and then in a cartoon voice, "Work, work, work!" using a high, sing-song tone or different accent or both. I assume you don't think this is something he's doing when trying to be funny or lighthearted, and he's done it so long that doesn't even realize when he does it?
Dissociative identity disorder comes to mind. Did he ever endure a lot of trauma, either as a child or in the military? DID is a way of suppressing painful or traumatic memories. The way he behaves doesn't sound like the classic description where someone manifests different, obvious personalities (a main one and sometimes a bunch of less prevalent ones), but possibly it might be related, or a very mild case. Part of what suggests this is that he never is angry. (I mean, everyone is angry sometimes. Someone who is overly sweet all the time seems like they might be suppressing normal reactions to life's upsetting moments, maybe because emotionally in the past it hasn't been safe to do so.) Does he laugh and so forth in the way you describe, when if he were a more average person he might be upset? If so, it could be a way to stuff anger or avoid it.
Anyway, whether or not that is what's going on, it sounds like you are going to difficulty convincing him that he does this laugh thing. I guess you could try to record him. Try not to be scared of it, apparently people with such disorders need the people around them to be supportive and calm. And odd though it seems to you, it doesn't actually sound dangerous.