The halacha (SA YD 244:1) is that one should stand up out of respect for a talmid chacham.
I remember hearing a comment (possibly in the name of the Brisker Rov) that one is really standing up for the Torah of the talmid chacham, not for him.
One practical implication is that a father talmid chacham wouldn't be able to refuse that his son stands for him since the son is standing for his father's Torah, not only for his father.
Is there such a source?
Shulchan Aruch Yoreh De'ah 242:32:
הרב המובהק שמחל על כבודו בכל הדברים האלו או באחד מהם לכל תלמידיו או לאחד מהם כבודו מחול ואף על פי שמחל מצוה על התלמיד להדרו (ואסור לבזותו)
A rav muvhak [someone from whom one gained a majority of his Torah] who forgoes his honour in all these matters [including standing for him (see 242:16)] or in one of them, to all of his students or to to one them, his honour is foregone. Even though he forgoes his honour, it is still a mitzvah for the student to grant him some form of respect (and it is forbidden to disgrace him).
So it would seem, according to the dichotomy which you presented, we are standing for the man himself and not for the Torah.
However, if we look at the source for this ruling in Kiddushin 32 we see that it is a little more subtle:
רב יוסף אמר אפי' הרב שמחל על כבודו כבודו מחול שנאמר (שמות יג, כא) ויי' הולך לפניהם יומם אמר רבא הכי השתא התם הקדוש ב"ה עלמא דיליה הוא ותורה דיליה היא מחיל ליה ליקריה הכא תורה דיליה היא הדר אמר רבא אין תורה דיליה היא דכתיב (תהלים א, ב) ובתורתו יהגה יומם ולילה
And Rav Yosef says: Even with regard to a rabbi who forgoes his honor, his honor is forgone, as it is stated: “And the Lord went before them by day” (Exodus 13:21). God Himself, the Teacher of the Jewish people, had forgone the honor due Him and took the trouble to guide the people. Rava said: How can these cases be compared? There, with regard to the Holy One, Blessed be He, the world is His and the Torah is His, and therefore He can forgo His honor. By contrast, here, is it his Torah, that the teacher can forgo its honor? Rava then said: Yes, if he studies, it is his Torah, as it is written: “For his delight is the Torah of the Lord, and in his Torah he meditates day and night” (Psalms 1:2). This indicates that at first it is “the Torah of the Lord,” but after he studies, it becomes “his Torah.”
Rava appears to be teaching us that we are indeed standing up for honour of the Torah, but inasmuch as the Torah "belongs" to the Rav, it is within his gift to forego the honour due.
Disclaimer: Joelk has already successfully addressed whether a Talmid Chacham can Mocheil on his Kavod as it is "His Torah", I am just here to take issue with the statement quoted that you are standing up for his Torah alone.
The Gemora in Gittin 31b implies that we stand up for the person rather than the just the Torah that he has acquired:
רב הונא ורב חסדא הוו יתבי חליף ואזיל גניבא עלייהו אמר חד לחבריה ניקום מקמיה דבר אוריין הוא א"ל אידך מקמי פלגאה ניקום
Rav Huna and Rav Chisda were sitting and Geniva (name) walked past. One said to the other "should we stand up for him as he is full of spiritual light i.e Torah."
The other replied "How can we stand up in front of someone who argues disrespectfully with Talmidei Chachamim (i.e Mar Zutra who was belittled by Geniva see Gittin 7a)?"
Indeed the Tashbeitz 1,146 brings such a conclusion from many citations all over Shas: https://www.sefaria.org/Gittin.31b.10?lang=he&with=Sefer%20HaTashbetz&lang2=he
So while its true that without the acquisition of Torah we don't stand up for him, we need both Torah and Middos - good attributes, we do not stand up for Torah if not accompanied by good Middos this is a misquote from the Brisker Rov.
