Women did not travel
I argued earlier that women did not travel (except in the company of male members of their households). Here I will first support this conclusion using data from Ignatius and Clement of Rome.
Clement (65), writing probably at the end of the first century, mentions three messengers: Claudius, Ephebus, and Valerius Vito. All three are men.
Ignatius, writing in the early second century, mentions 12 messengers/envoys by name and they are all male: Burrhus (Eph 2; Philad 11; Smyrn 12), Crocus (Eph 2; Rom 10), Onesimus (Eph 2, 6), Euplus (Eph 2), Fronto (Eph 2), Damas (Mag 2), Bassus (Mag 2), Apollonius (Mag 2), Zotion (Mag 2), Polybius (Tral), Philo (Philad 11; Smyrn 10, 13), and Rheus Agathopous (Philad 11; Smyrn 10).
Furthermore, Ignatius's letter to the church of Rome was delivered by "men of Ephesus" (Rom 10). Also, Ignatius assumes that enjoys that will be selected by the Philadelphians (Philad 10) and by Polycarp (Poly 7-8) will be male.
Ignations mentions 7 individuals who, as far as we know, have not travelled. 3 of them are women, shown in red: Polycarp (Poly); Procurator's lady (Poly 8), Attalus (Poly 8), Alce (Poly 8; Smyrn 13), Tavia (Smyrn 13); Daphnus (Smyrn 13); Eutecnus (Smyrn 13).
All this confirms what we deduced previously from Acts, the letters of Paul, and the disputed letters of Paul: women did not travel (except with family).
Greetings are sent between individuals who knew each other
Ignatius wrote his first four surviving letters from Smyrna where he must have spent considerable time (presumably while waiting for a ship and the right winds). Two of his three later letters were sent to Smyrna (Smyrnaeans and Polycarp) and these are the only letters sent to a place where he spent considerable time (he had not been to Rome, Ephesus, Magneia, or Tralles, and there is no evidence that he would have been allowed to tarry in Philadelphia). It is surely no coincidence, then, that all those whom Ignatius greets individually (the non-travelers listed above) are in Smyrna. His personal acquaintance with them makes him mention them individually.
The only time when an individual joins with Ignatius in sending greetings is when Philo greets the Smyrnaeans (Smyrn 13). Presumably Philo has stayed in Smyrna on his journey to catch up with Ignatius.
The evidence from Ignatius therefore confirms the common-sense view that greetings are sent to and from individuals who have met.
Implications for the identities of the greeters in Rom 16:21-23
Just as Philo, mentioned above, was a man, so too were all those who send greetings in Rom 16:21-23, as well as the greeters in Philemon 23-24. This is no co-incidence. Only men travelled and therefore only men would have met those addressed. Lucius (Rom 16:21) and Luke (Philemon24) were therefore travelers and this supports the view that they were the same person and the author of Acts. I have argued this point in more detail before, here, but without the supporting data from Ignatius and Clement of Rome.