Great post. Looking back at historical serial killers (I don't want to call them "historic" serial killers!), signatures are often things like posing the body after death, cleaning the body, the specific order of doing things (binding, etc.). Think about it this way: your signature in handwriting is unique and it's something above and beyond just writing your name. The cursive and flourishes are not necessary but they are part of how you identify yourself. It is similar for criminal signatures.
Great analogy. And yes - we've had posters on the Delphi threads before who've speculated things like, maybe the killer left flowers behind, or a deck of cards (trying to speculate on what Ives meant by a large amount of physical evidence, and not what one would imagine). But signatures - again, as criminologists use the term - is usually not about objects, it's about behaviors.
Signatures that are "commonly" seen (odd to call it common as these are the rarest of offenders who are leaving signatures) are mutilation, necrophilia, insertion of objects, posing the body in order to degrade the victim (note: staging the body to mislead the investigation is a different type of act, not signature but MO), cutting or shaving the victim's body hair, taking trophies, use of bindings and restraints (seen in most child murders perpetrated by strangers), and particular forms of violence aimed at depersonalizing the victim. Of course this list is not exhaustive but it's typical.
All JMO but if you want to read more this is a god resource: Articles