On first glance, the answer that came to mind was accidental death or serious injury due to sheer incompetence, like walking off a cliff. Something that has a massive survival cost and only communicates failure seems like it couldn't be signaling. Mistakes are revealing, after all. But this kind of signaling happens all the time, mostly as a flawed means of signaling courage or simply drawing attention.
It struck me then that the question of what is "least signaling" may not be useful for determining states of mind, that every behavior can be an attempt at signaling. All that changes is the size of the audience and the success of the signaling. Conversely, a behavior that is usually associated with signaling can occur for perfectly honest or private reasons. (This is the pretense of polite society, that someone "meant nothing by it" even when "it" is dressing in a frock coat and top hat or, alternatively, stripping half naked. But that is for another thread.) The point is we are not bound to always think in a signaling way when we're involved in behavior that readily signals.
I take it as obvious that signaling is an important function in many human behaviors. That is, the details of many of our behaviors make sense as a package designed to persuade others to think well of us. While we may not be conscious of this design, it seems important nonetheless. In fact, in many areas we seem to be designed to not be conscious of this influence on our behavior.
But if signaling is not equally important to all behaviors, we can sensibly ask the question: for which behaviors does signaling least influence our detailed behavior patterns? That is, for what behaviors need we be the least concerned that our detailed behaviors are designed to achieve signaling functions? For what actions can we most reasonably believe that we do them for the non-signaling reasons we usually give?
You might suggest sleep, but others are often jealous of how much sleep we get, or impressed by how little sleep we can get by on. You might suggest watching TV, but people often go out of their way to mention what TV shows they watch. The best candidate I can think of so far is masturbation, though some folks seem to brag about it as a sign of their inexhaustible libido.
So I thought to ask the many thoughtful commentors at Less Wrong: what are good candidates for our least signaling activities?
Added: My interest in this question is to look for signs of when we can more trust our conscious reasoning about what to do when how. The more signaling matters, the less I can trust such reasoning, as it usually does not acknowledge the signaling influences. If there is a distinctive mental mode we enter when reasoning about how exactly to defecate, nose-pick, sleep, masturbate, and so on, this is plausibly a more honest mental mode. It would be useful to know what our most honest mental modes look like.