A. K. Flowerree and Mark Satta have a brief discussion of virtue-signaling at the blog "Justice Everywhere", arguing that intellectual humility should generally require us to avoid making judgments about whether someone is virtue-signaling. Unfortunately, they too uncritically follow Neil Levy's highly eccentric account of virtue-signaling, and therefore almost everything they say about the topic is incorrect.
(1) They gloss 'virtue-signaling' as "using moral language to make oneself look good". This is a useless description that covers many things that nobody counts as virtue-signaling (e.g., defending oneself by law and evidence in a court). Part of the problem, I think, is that they follow Levy in misdividing the term. Levy reads 'virtue-signaling' as {virtue}-{signaling}, when in reality the term should be broken up as {virtue-signal}ing. Virtue-signaling is the behavior in which one treats virtue-signals as if they were virtuous character; it involves a deliberate emphasis on appearance (virtue-signals) rather than the substance of actual virtue. This is the point of Bartholomew's widely discussed essay and book (which, despite Levy's attempt to dismiss them on the basis of a few similar but scattered expressions prior, are the primary reference-points for how the term has been used). It is also clear that this accords with most, and allowing for the ordinary stretches of colloquial use, perhaps almost all uses of it in ordinary conversation.
(2) They conflate 'virtue-signaling' with the 'moral grandstanding' of Warmke and Tosi. Levy does this, too, and it is incorrect. Warmke and Tosi, while recognizing some family kinship and possible overlap, do not equate 'moral grandstanding' with 'virtue-signaling'; that's in fact why they call it 'moral grandstanding' rather than 'virtue-signaling'. Nor should they, even if they did; some forms of moral grandstanding are quite clearly not virtue-signaling (e.g., arrogantly pointing to your actual moral accomplishments to assert superiority over others) and some forms of virtue-signaling are quite clearly not moral grandstanding (e.g., some kinds of corporate advertising, which, in fact, are some of the paradigmatic cases).
On the basis of (1) above, they argue,
The goal of trying to make oneself look good through one’s moral talk is the constitutive feature of virtue signaling. Thus, in order to recognize that someone is virtue signaling, you need to be able to identify that they have this specific goal.
As noted above, it's simply incorrect to say that "trying to make oneself look good through one's moral talk is the constitutive feature of virtue signaling". But this is wrong in a more direct sense, as we can see when we look at advertisement. (The failure to consider advertisement practices, despite the fact that they are perhaps the most obvious field in which virtue-signaling occurs, is a failure that Flowerree and Satta again share with Levy.) First, note that talk is not necessary. When Frito-Lay decorates its Doritos bags with rainbow flags in honor of pride month, they don't even have to say anything about it to make this a case of virtue-signaling. Nor, second, do we need to exert any serious effort to recognize it as such; Frito-Lay is a corporation, engaging in a marketing campaign, not a person actually exercising any virtue, and thus we know that the appearance of good character is in fact just Frito-Lay executives deliberately marketing Doritos as pro-LGBT in the attempt to persuade people that eating Doritos is somehow a way of supporting gay pride. Further, we can clearly recognize, when we reflect on the matter, that eating Doritos does not itself have much to do with LGBT concerns, and that nothing about Frito-Lay or its products would fundamentally change if they started marketing their chips as a way of opposing gay pride.
The point does not shift much when we move from corporate virtue-signaling to individual virtue-signaling. I don't actually need to know whether someone intends to make themselves look good with moral talk; I need to know whether they are treating signals of virtue as if they were virtue. This is obvious in consumer practices, which are the individual cases most closely allied to the corporate virtue-signaling cases, but it is true generally. You don't need to know someone's goal in virtue-signaling; you need to know that they are using virtue-signals as if they were themselves good character.
Likewise, they say:
As Tosi and Warmke point out, the virtue signaler is not likely to get the moral credit they seek by making direct claims about their moral virtue. Saying “I’m a moral exemplar!” is a poor strategy for getting others to think you are morally exemplary.
This may be true of moral grandstanders; it is not necessarily true of virtue-signalers. Virtue-signaling may be subtle, but it does not depend on subtlety. If I put up a sign in front of my house, saying, "In This House, We Believe that Kindness Is Everything", I am putting up a virtue-signal. Nothing about having a sign like this in front of your house makes you a kind person; it is not itself a kind deed. But I am making what everyone would think is a direct claim of moral virtue, because the view most people would take is that if I had this sign outside my house and were a cruel or even just not particularly kind person, I would be a hypocrite. And when you realize this, you realize that (1) all sorts of people do this all the time and (2) it is not a bad strategy at all because it often works. If a company says in its advertisements, "Black Lives Matter", very few people look to see whether the company policies are even consistent with this self-presentation, even setting aside that the self-presentation itself is clearly a marketing campaign, and even if they did, it would still work in lots of cases. Putting yourself explicitly on the "Kindness Is Everything" team is actually quite effective even when people are inclined to be cynical; it will certain get you further than admitting that you are often unkind. Most of our dealings with most people (or corporations) most of the time are with them as they appear; if you're very unsubtle about it, you might raise some eyebrows, but most people are simply not going to pursue the matter very far. Even when we are skeptical of them, we often take people's self-presentations as our starting-point.
The thing of it is, virtue-signaling can be entirely sincere. People who put up "Kindness Is Everything" signs where everyone can see them are not generally trying to hide their secret depths of cruelty. This is why virtue-signaling is such an important issue in advertising. People really do buy rainbow-flag products, and they may well believe, sincerely, that by doing so they are supporting LGBT rights. But actually they are just buying products, whose actual connection to LGBT rights they have usually not investigated, and in many cases they don't ever do much else. The same is sometimes true of Christians who put fish-symbols on their cars and don't do much else of noticeably Christian character. They are using virtue-signals as if they were substantive virtuous deeds themselves because they have sincerely confused virtue-signals and virtuous deeds. That's why virtue-signaling is so common, despite being so criticized. You can often get away with it, and people are often not maliciously or even deliberately doing it.
Flowerree and Satta do manage to be correct in saying that we have a greater tendency to accuse our 'outgroup' of virtue-signaling than of doing the same to our 'ingroup'. But this is (contrary to what Flowerree and Satta suggest) true of almost all criticism whatsoever. People find it easier to criticize the outgroup of basing their reasoning on false claims; people find it easier to criticize the outgroup of reasoning poorly; people find it easier to criticize the outgroup of misrepresenting the other side. There is nothing particularly distinctive about criticizing people for virtue-signaling in this, and if you allow one kind of criticism, you should allow the other.