I wasn't able to edit the post;https://en.wikipedia.org/wiki/Expiration_Date_(novel
I believe the idea is, the sequence of letters seemingly has significance to anything that can comprehend language. In observation of the sequence, the attention of the observer is captured as it/he/she attempts to understand the palindrome. The modality seems to be exactly that, to capture the attention and instigate a search for meaning. As more attention is given to the palindrome the basis for meaning is established by the fruitfulness of the search being countered by the illusion of meaning. Sort of an infinite regression (https://en.wikipedia.org/wiki/Infinite_regress
As human beings, we inherently look for meaning through perception of symbols. As such we are able to quickly discern between significance of meaning and actuality.
Why do human beings do this? It all comes down to how we draw meaning from the environment around us. If we were orbiting the Earth in the ISS, our perception of the surface from our visual perception (at least during day time) would amount to a conclusion where the presence of life on the planet below would be terribly difficult to spot. This is due to our distance from the humans on the surface. A similar parallel is found with us and bacteria. Although we cannot necessarily see a Streptococci organism, they still exist everywhere.
This perception of human scale is an understanding inherent to our brain. The phenomena is known as scale invariance. https://en.wikipedia.org/wiki/Scale_invariance
How does that tie into the pallindromes? I believe that whichever entity can comprehend reality can only do so by attaching themselves to a point in scale invariance so as to create a symbol or landmark for our human scale to perceive reality at our perception scale (sort of like an anchor point). In doing so, it can make itself understand this reality.
The palindromic traps I've mentioned earlier perhaps are a means to confound such attempts at perceptive understanding (see the infinite regress mentioned earlier).
Why are we seeing 11:11? Are we entities albeit caught in some other kind of palindromic trap - looking for meaning of a seemingly infinite search?