I found your link to the Constructs often confused with Alexithymia very useful.Interesting.
Those questions seem to assume a whole lot and could easily confuse stoicism with emotional suppression and/or with alexithymia (some people see emotional suppression as distinct from alexithymia, others see it as part of/causing alexithymia, apparently.....link: Constructs often confused with Alexithymia).
I nthink a person could know they are not okay (awareness), know how they are not okay (recognition/identification/understanding of feelings) and be able to describe that others but choose not to for all kinds of reasons.
It breaks down into various catagories what is and is not.
The short quiz questions that showed Alexithymia, when I review why I answered the way I did
would fit first Stoicism- knowing full well what I feel, but, don't want to let it show to the outward world.
Then as stated in the article: Apathy- not reacting to situations in the world around me.
And also repression to emotions that might arise inwardly from personal traumatic situations.
This line from the Repression definition fits quite well:
"In repression, the patient subconsciously understands the nature of his or her feelings and (sometimes) the cause of those feelings, and this subconscious comprehension generates neurotic conflict. He or she gives out subtle clues about their hidden feelings, by means of sublimated fixations or dream content."
Very interesting read on the seperate catagories.