After several weeks of struggling over this Gemara, I've found a possible explanation.
Note: my Hebrew is still a work-in-progress. I might have read things different/interpreted it a my own way. Please feel free, I even encourage all of you, to improve translations/literal translations/interpretions of the quoted/cited sefer.
Rabbi Menachem Brod, spokesman of Chabad youth movement center Tze'irei Agudas Chabad in Israel and the editor of the nationally distributed Chabad weekly pamphlet Sichat HaShavua wrote an sefer called: "ימות המשיח"- Yemos HaMoshiach - the Era of Moshiach. Let's dissect and analyze the piece, bit for bit.
The Gemara states that three things come בהיסח הדעת - Behesech Hadaas- unexpectedly. One of these three is Moshiach.
This is as in that practice of Rabbi Zeira, who, when he would find
Sages who were engaging in discussions about the coming of the
Messiah, said to them: Please, I ask of you, do not delay his coming
by calculating the end of days. As we learn in a baraita: There are
three matters that come only by means of diversion of attention from
those matters, and these are they: The Messiah, a lost item, and a
scorpion. (Sanhederin 97a)
The Lubavitcher Rebbe translates the words "behesech hadaas" somewhat different than others. The Rebbe says:
This teaching does not mean that a person should not (G‑d forbid) think about the Redemption and anticipate its coming. It means that though his reason sees no possibility for Redemption, a Jew persists with an intense belief that transcends his reason. This meaning springs directly from the Hebrew idiom בהיסח הדעת (here translated “unawares”), which literally means “with one’s reason set aside.” (Likkutei Sichos vol. 5)
So, according to the Rebbe, Behesech Hadaas does mean unawareness (peshat reading). However, it should be read as "with one's reason set aside". That's the basis for the explanation of Rabbi Brod in sefer Yemos HaMoshiach.
Beginning from page 59, Rabbi Brod says that daily, we anticipate the coming of Moshiach. We pray about the coming of Moshiach/Redemption multiple times a day. We "express a immense longing for redemption", says the author. Does all of this become puzzling because of the statement of our sages that "Moshiach comes unexpectedly"?
Rabbi Brod goes on to cite a Gemara that talks about Rabbi Zeira, encountering people that were engaging in discussions about the coming of Moshiach (Sanhedrin 97a). The Gemara says that:
when he (Rabbi Zeira) would find Sages who were engaging in discussions about the coming of the Messiah, said to them: Please, I ask of you, do not delay his coming by calculating the end of days.
Rabbi Brod quotes Rashi to explain that this Gemara was referring to people that were busy calculating when Moshiach would come. As Rashi says (ad loc.):
דמעסקי ביה - לידע מתי יבא
Rabbi Zeira responds to these people with:
I ask of you, do not delay
Why? Because "three things come unexpectedly, one of which is Moshiach".
In sefer Yemos HaMoshiach, the author goes on to explain that even "these three things come when not expected", that does absolutely not mean that we should not think about redemption and the coming of Moshiach (p. 60).
שני הפרטים האחרים באותו מאמר מציאה ועקרב ממחישים עד כמה אין המחשבה והציפייה לגאולה סותרות את היסח הדעת' אדם יכול להתהלך כל היום במחשבה שהוא רוצה למצוא מציאה וכי מפני זה לא יהיה רגע המציאה הפתעהנ או אדם שמהלך בשדה מתוך מודעות מתמדת לסכנת העקרבים שבסביבה האם יוכל לדעת מראש מתי בדיוק יעקוץ אותו עקרבנ כך גם הגאולה אנו צריכים לחשוב עליה כל הזמן לצפות לה להתפלל עליה להתכונן לקראתה ועם זה ברור לנו שהיא תבוא בהפתעה A person can walk around all day thinking that he wants to find the object he lost, does that mean that when he finds the lost item that he is not surprised? Or a person who walks in a field with a constant awareness of the danger of scorpions in that area, will he be able to know in advance exactly when a scorpion arrives and sting him? So is redemption - we need to think about it all the time, expect it, pray for it, prepare for it. Even then will it come as a surprise.
The author quotes an explanation of the sefer מאורי החסידות. I am not familiair with that sefer and exact place of the quotation. If someone could please add that in, that would be wonderful.
The sefer מאורי החסידות says that when a Jew looks around him and he does not see (signs) that redemption is coming soon but nevertheless has faith in that it will come, because Hashem says so. That is what בהיסח הדעת - Behesech Hadaas means. He put's away his thoughts and keeps faith in that even though we are still in galus, redemption will come. Somewhat related to this is the Cognitive dissonance-theory.
הדעת זו מתנה מלמעלה שהאדם עצמו אינו יכול להגיע אליה באמצעות דעתו ושכלו אלא הקב"ה נותנה לנו באופן שלמעלה מהדעת It is a gift from above, which a person by himself cannot reach through his own mind and intellect. Nevertheless, G-d gives us the understanding
We can't understand that Redemption is coming, but we are meant to put away this thoughts, e.g. behesech hadaas, because we know that it comes.
Rabbi Brod then cites the Rebbe in Toras Menachem (תורת מנחם התוועדויות - חלק י"א) (could not find it either) and says:
Distraction is the highest form of waiting for Moshiach (תורת מנחם כרך ט עמ' p. 111)
We must distract ourselves from the thought that we want Moshiach because then, everything will be "okay". During Covid, people often said "I want Moshiach because then this is all over". This should not be the thought. Rather, we must want redemption because that is the end-goal of Hashem, e.g.:
שתושלם הכוונה האלוקית בבריאת העולם להיות לו יתברך דירה בתחתונים G-ds intention in the creation of the world was to have a dwelling in the lower place(s).
The author ends with the explanation that when the situation is such that the mind and intellect see no place for redemption to come - this "distraction" is a sign of the coming redemption. This is בהיסח הדעת - Behesech Hadaas.