I'm reviewing the historical original ASCII standard.
The 1963 iteration was still mostly TTY orientated and got only partly adaption with TTYs. Computer use was incosistent, especially since most logical control characters were not standardized at all.
There are many control characters. Does anyone know the history of them
Except for the Sn series they're all TTY related and direct descendants of other prior codes and applications (mostly ITA2 as base and FIELDATA for computer use). You might want to consultate other teleprinter setups and manufacturers here, as well as their protocols.
and where finite state machines that made use of them may be documented?
Mind to explain what kind of purpose the a state machine you're asking for should have? Without that question doesn't make much sense.
I ask because it's not in the document with the ASCII standard I found.
As it's not any business of the standard? Keep in mind, back than standards were made for practical use by engineers, not theoretical clean room definitions. All control codes used are of obvious meaning to a 1960s user, so no need for much explanation, beside spelling their function that is.