I am sorry to be coming so late to the party. “Virtue signaling” is a term I heard for the first time today. I know. I ought to get out more.
It seems to me that “virtue signaling” is an accusation one person might make against another. The accusation is that you are signaling that you possess some virtue; you are signaling it, but not doing it. Or, more seductively, you are signaling it rather than doing it.
“Seductive,” (above) which I treat as a genuinely heavyweight word, introduces the idea that its use leads you astray  and as a result of this change, you begin to attend to the motives of the person rather than to the effect of the action. Here is an example.
So A hammers a “Black Lives Matter” sign into the front yard. B stops by and says, “Oh, I see that you are claiming to have the virtue of anti-racism.” A says, in other words, “We need to do something about the callous treatment of black protesters.” B says, “Let’s talk about why you want place before the neighborhood the claim that you are a virtuous person.” A says, “Let’s talk about a public crisis.” B says, “No, let’s talk about a private motive.”
And there goes the statement A was hoping to make and all the actions that might have followed the statement. So we might consider what B gets out of the exchange. If B is a racist—or if he is just sick of race being considered as the only relevant political category—B gets the satisfaction of blunting the effect of the sign. Having successfully changed the subject from whether black lives actually matter to whether A is spuriously claiming a virtue he has no right to claim, he can conclude the exchange with satisfaction.
If B is sick and tired of A’s posturing, the satisfaction he takes might be even more direct. A is making yet another claim to virtue! Does he really never get tired of pretending that he is more virtuous than the rest of us? But this time, in using a public claim as his virtue, he had opened himself up for rebuke and that’s why I am here.
Those are not merely two examples of B’s retaliation, they are two categories of B’s retaliation. This may be an interpersonal squabble that has nothing to do with the public issue or it may be principally a public issue and changing it into a personal claim reduces the effect it might have had on the issue itself.
Actually, when the question of drawing attention to your own virtues came to my attention, the language that emerged first was from the Sermon on the Mount. It was, “When you are fasting, do not put on a gloomy look as the hypocrites [play actors] do: they go about looking unsightly to let people know they are fasting.” They are virtue signaling, in short. 
Jesus offered an oddly configured alternative. He said that if you were in the market for moral credit, you could look for it from your peers or from God. It is, however, one or the other. If you are fasting—this is a religious duty, not weight control—for the purpose of getting everyone to notice how holy you are, then that is the reward you will get. If you are fasting as a way of coming close to God and if you take measures to conceal from your peers that you are doing that, then God will reward you. But it’s one or the other.
That seems clear to me, probably because I have never lived in a society where fasting as a religious duty was practiced. I find more practical examples more confusing. Who would have thought it?
I have lived in a society where other things were prized, however. Take purity in purchasing foods, for instance. You could be “righteous” for purchasing only virtuous goods.  You could be righteous by purchasing virtuous goods from virtuous stores. You could be righteous by investigating the conditions under which the food was produced and by buying only foods produced without the exploitation of workers. You could be righteous by buying food only from companies who use their profits in ways you approve.
Have you begun to roll your eyes yet? I have heard every one of these defended as what you should do if you really care about how you get your food. I have heard every one defended on the grounds that not doing that particular one amounted to being complicit in whatever evil was being contemplated.
In other words, virtue signaling doesn’t have to be about race. It can be about religious practices, as the example of fasting makes clear, or about food consumption, as the example of consumer politics makes clear.
The hard thing about virtue signaling is that it is a part of human communications. That means that “virtue” can be proclaimed by A or can be attributed by B. A may have an intention or an intention may be attributed to A by B. That’s how human communication works.
Take John Hancock for instance. In the movie, 1776, Hancock as the presiding officer of the Second Continental Congress, was the first to sign the Declaration of Independence. Further conversation ensues and Hancock is forced to remind the other delegates that if they were discovered right then by the British solders, Hancock’s name was the only one on the document. This was received in the movie with widespread laughter.
In Stan Freberg’s treatment, on the other hand, the Declaration of Independence is a “petition” that Jefferson is “circulating around the neighborhood” and he is asking a very snarky Ben Franklin if he would like to sign it. Franklin says he would like to read it first, and when he unrolls it, he sees Hancock’s signature. “Look at that show-off Hancock” he explodes. And then, more reflectively, “Pretty flamboyant signature for an insurance man.” 
These two instances illustrate what this aspect of human communication is like and why “virtue signaling” will always be an issue. Hancock is putting “his life, his property, and his sacred honor” at risk, as are all the signatories. It is an act of daring and, from the American perspective several centuries later, of virtue. Franklin’s complaint—based in the culture of the 1950s—is that Hancock is showing off. Hancock is virtue signaling. That is the motive attributed to him by Freberg’s Franklin. Moral oneupsmanship is being attributed to Hancock by Franklin.
Hancock intends; Franklin attributes. It’s human communication. And, as Lord Alexander Chung-sik Finkle-McGraw says, “People are naturally censorious.” 
So there us nothing you can do to absolutely prevent someone from attributing “virtue signaling” as your real private motive..You can make it less likely, of course, by a) not having any enemies, b) not being generally known as someone who dearly loves his virtues, or c) making it a practice to pursue your goals in the company of like-minded others.
Or maybe just not caring.
 The root is ducere, to lead. It has nothing at all to do with sexuality, the common usage notwithstanding. You can be drawn away (se-) from any path you ought to be traveling.
 In more academic settings there is the question of what is a signal and what is a sign. I would love to get into that another time and if I do, I will cite Jesus’ admonition that his disciples should “Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven” I felt the need here to resort to the King James Version
 You get to choose the virtue: low sugar, low salt, low carbs, organically grown, eggs from free range hens, etc.
 One of the many Freberg jokes that mixes together the 1950s and the 1770s. Freberg is playing on the idea that more people will know John Hancock Insurance than John Hancock.
 One of my favorite comments from Neal Stephenson’s The Diamond Age. I have cited this so often that I can put this character’s name in confidently without looking it up.
“Hancock intends; Franklin attributes.”
I came to believe several years ago that the most pernicious disease in America was not any of the physical or mental health issues that afflict people, but rather what I came to think of as the willingness (eagerness, even) of many people to invent motives for other people.
If we combine your formulation with mine, we could get “the invention of intention”. This isn’t quite as snappy as I’d like, but it’s getting there.
One way for person A to deal with person B is for A to ask B where the hell he thinks he gets the right to assert what A’s intentions are. That at least might have the benefit of shifting the ground on which they are arguing.
Peace, eric =========