There is nothing special about self-reference in this sense, just about references of any kind. Nor do I agree with Derrida that this is necessarily about 'seriousness', given that the authenticity of documents as proven by signing can be a powerful force taken in dreadful earnest.
Lacan's notion of the master signifier as an empty object is another way of looking at this. No mark has meaning except within a "living symbolic realm" -- a context of overlapping compromises which is socially determined and shifts. I cannot put it better than I did in this (unpopular) answer https://philosophy.stackexchange.com/a/23974/9166
Signatures are meaningful because they are accepted, not because they contain meaningful proof. There is a feedback loop that continually changes what range of images will appear to be a given individual's signature and will be acceptable at a given time. As a person ages, for instance, and their hand may shake. At the other end of life, as their personality evolves, their style will affect all of their writing. Or they may simply decide to change their signature on a whim, but then give the signature in the presence of witnesses, or on something no one else would bother to sign, or, as in Derrida's case in a context where there is no ambiguity about the source of the mark because the signed work is so characteristic of the individual. It is not the form of the signature that ever actually matters, only the context and the range of other contexts in which that signature has occurred.
This is just a very concrete example of how concepts are maintained in general. No concept has content except as a stable point in a feedback loop that maintains the homeostasis of the concept itself. The actual content of any reference, or indeed any idea, stripped of all its embedding information is empty. We make shared ideas by shaping our ideas according to other ideas we got elsewhere...
This notion undercuts the idea that philosophies, especially those including ontologies cannot really ever be well-founded on a strictly logical base and derived hierarchically. There is no up or down at some level of detail.