The term was coined nearly 40 years ago by a prominent cardiologist, who noticed that all of his heart disease patients had common behavioral characteristics, the most obvious being that they were in a chronic rush.
I think it is debatable whether the adjunct in bold is a true absolute clause. It meets some of the criteria by virtue of being non-finite, supplementary, and subordinate in form, but absolutes have their own subject and thus have no syntactic link to the main clause. In this case the subject is the fused modifier-head "obvious" which is interpreted anaphorically as "most obvious of them", i.e. "most obvious of the characteristics". It could be argued that since the subject is not truly overt, it fails to qualify as an absolute.