I'm looking for a noun which is kind of word or phrase that is used to indicate the existence of some unspoken knowledge that the speaker has.
For example:
Her use of the the word "pincushion" was a deliberate ___________ intended to let him know that she knew his secret identity, without alerting those she suspected to be listening in.
I've a feeling this word begins with an S and has 3 or 4 syllables, but am drawing a long blank in my memory...
Shibboleth comes close, though it's not used in the way you intend. Historically, it was used as a proxy test related to whether the person started the word with the sh- sound or the s- sound.
Shibboleth noun A custom, principle, or belief distinguishing a particular class or group of people, especially a long-standing one regarded as outmoded or no longer important: liberal shibboleths about education - ODO
A shibboleth ... in its original signification and in a meaning it still bears today, is a word or custom whose variations in pronunciation or style can be used to differentiate members of ingroups from those of outgroups. Within the mindset of the ingroup, a connotation or value judgment of correct/incorrect or superior/inferior can be ascribed to the two variants. - wikipedia
You might be looking for cipher, "a coded message" (sense 7, here). It begins with an /s/ sound and works in your context:
Her use of the word "pincushion" was a deliberate cipher intended to let him know that she knew his secret identity.
Intimation, meaning "the action of making something known, especially in an indirect way" (here), also works in your context.
Other suggestions:
Wink works especially well, since winks are usually done on the sly, under the radar of others who are around:
Her use of the word "pincushion" was a deliberate wink intended to let him know that she knew his secret identity.
"subtleness" (or "subtlety") seems to be the word you're looking for.
"Her use of the the word "pincushion" was a deliberate subtleness/subtlety intended to let him know that she knew his secret identity, without alerting those she suspected to be listening in."
- subtleness - the property of being subtle, of avoiding brute force and instead being clever or skillful.
"The movie was praised for the subtleness of its themes. None of it came off as being too preachy."
"subtlety" is a good fit too.
I think tell works best here
to give information to (someone) by speaking or writing
Merriam-Webster
If there is an agreement between the speaker and listener (or group) beforehand, you might call such a word a dog-whistle, implying something that you know the speaker will hear a certain way that others will not. This term is often used in politics, for example, where one might, say, accuse a right-wing politician of using a term like "limiting Israeli expansion" as a dog-whistle to his anti-semitic supporters.
