I originally only knew of the one and I thought it was maybe catching her in a moment of thought. But then I saw a couple more of two other ladies holding the stylus to their mouths in the exact same way. Is there a reason they are posing this way? Does it have some kind d of meaning? Or was it just a popular way to pose for a portrait? Stylus to mouth https://imgur.com/gallery/bNdSAd6
I'm not sure about the specific meaning of holding a stylus to the mouth (beyond it looking very contemplative) versus holding it up in another way, but there are a few different interpretations for inclusion of a stylus in paintings of women. The first is that these are portraits that either show women who are displaying their literacy--either as writers/poets or as being involved in keeping accounts for a business--or that they depict Muses with the stylus as an attribute.
The portraits you included provide two good examples to illustrate these. On the left, you have a fresco from Pompeii now in the National Archaeological Museum at Naples, often called either "Woman with a Stylus" or "Sappho". Most modern scholars identify her as a Pompeian businesswoman because of the usually temporary, account-keeping purposes of the wax and wood tablets she holds in her other hand, but some still believe her a portrait of a famous woman author (1). In antiquity, she was paired with a male tondo portrait as well, who carried a scroll (a more permanent written document) that makes the pair iconographically closer to the couple's portrait on the bottom right of your photo mosaic.
The couple's portrait, which comes from Pompeii VII.2.6, is often either called "The Baker and his Wife" or "The Portrait of Terentius Neo". These identifications are based on some archaeological evidence, but with plenty of room for doubt. The portrait comes from the atrium (main reception area) of a house that was partially remodeled into a bakery, and had an election slogan in support of a local candidate for the aedileship signed by Terentius Neo. If the portrait represents a baker and his wife, then it probably shows their business acumen and at least a pretension to financial success. This portrait would have been visible to any visiting clients of the household, for example, which a successful business owner might have.
The similarity in poses between these paintings might mean a couple of different things as well. On a practical level, artisans in Pompeii seem to have used copybooks as design templates that they could combine into different overall schemes and customize as needed (2, 3 on painting practice by Roman artisans and the use of copybooks). In a more general sense, emulation was pretty common practice in Roman art--a high class matron might adopt the same hairstyle as the Emperor's wife, or have a statue made up of herself with the body of Venus. Portraits "in the guise of" someone else were not uncommon, so a similar pose might also indicate a particular role (and not necessary a role the person plays in reality).
This leads to the argument put forward by Elizabeth A Meyer that most of these images depict Muses--or women taking on the role of Muses--rather than portraits of women who are displaying their real-life literacy skills (4). Meyer's article is a very in-depth treatment of the appearance of writing instruments in Roman paintings, and discusses eight examples of women holding a stylus. She points to iconographic similarities of these portraits to representations of the Muse Polyhymnia alongside male (scroll-bearing) poets, and comes to the conclusion that the paintings do not represent realistic depictions of literate women, but rather abstracted generic portrait types replicated from models (either copybooks, or just emulation). I'm not sure I subscribe fully to Meyer's argument, as it would be wholly unsurprising to find women in Pompeii keeping business accounts and having their portraits made, but it is very detailed and interesting, and definitely brings up a kind of blurring between the representational and abstract impulses that coexisted in Roman art.