Servius on Vergil, Aeneid
For there were four things among the Romans that were related to showing respect: to dismount from your horse, to bare your head, to move out of the way, and to stand up. Even the heralds who preceded magistrates were said to shout these instructions.
quattuor namque erant apud Romanos quae ad honorificentiam pertinebant: equo desilire, caput aperire, via decedere, adsurgere. hoc etiam praecones praeeuntes magistratus clamare dicebantur.
Aulus Gellius, Attic Nights
2.2 (tr. J.C. Rolfe), discusses two of these marks of respect (standing up and dismounting):
What rules of courtesy should be observed by fathers and sons in taking their places at table, keeping their seats, and similar matters at home and elsewhere, when the sons are magistrates and the fathers private citizens; and a discourse of the philosopher Taurus on the subject, with an illustration taken from Roman history.
 The governor of the province of Crete, a man of senatorial rank, had come to Athens for the purpose of visiting and becoming acquainted with the philosopher Taurus, and in company with this same governor was his father.  Taurus, having just dismissed his pupils, was sitting before the door of his room, and we stood by his side conversing with him.  In came the governor of the province and with him his father.  Taurus arose quietly, and after salutations had been exchanged, sat down again.  Presently the single chair that was at hand was brought and placed near them, while others were being fetched. Taurus invited the governor's father to be seated;  to which he replied:  "Rather let this man take the seat, since he is a magistrate of the Roman people." "Without prejudicing the case," said Taurus, "do you meanwhile sit down, while we look into the matter and inquire whether it is more proper for you, who are the father, to sit, or your son, who is a magistrate."  And when the father had seated himself, and another chair had been placed near by for his son also, Taurus discussed the question with what, by the gods! was a most excellent valuation of honours and duties.
 The substance of the discussions was this: In public places, functions and acts the rights of fathers, compared with the authority of sons who are magistrates, give way somewhat and are eclipsed: but when they are sitting together unofficially in the intimacy of home life, or walking about, or even reclining at a dinner party of intimate friends, then the official distinctions between a son who is a magistrate and a father who is a private citizen are at an end, while those that are natural and inherent come into play.  "Now, your visit to me," said he, "our present conversation, and this discussion of duties are private actions. Therefore enjoy the same priority of honours at my house which it is proper for you to enjoy in your own home as the older man."
 These remarks and others to the same purport were made by Taurus at once seriously and pleasantly.  Moreover, it has seemed not out of place to add what I have read in Claudius about the etiquette of father and son under such circumstances.  I therefore quote Quadrigarius' actual words, transcribed from the sixth book of his Annals: "The consuls then elected were Tiberius Sempronius Gracchus for the second time and Quintus Fabius Maximus, son of the Maximus who had been consul the year before. The father, at the time proconsul, mounted upon a horse met his son the consul, and because he was his father, would not dismount, nor did the lictors, who knew that the men lived in the most perfect harmony, presume to order him to do so. As the father drew near, the consul said: 'What next?' The lictor in attendance quickly understood and ordered Maximus the proconsul to dismount. Fabius obeyed the order and warmly commended his son for asserting the authority which he had as the gift of the people."