One way to identify a nominative absolute is to add a verb; one can always create a sentence out of a nominative absolute by adding one verb (generally a form of to be).
Their manes flowing, the horses ran from the burning barn.
Nominative absolute: Their manes flowing.
With a verb added: Their manes were flowing.
Stephen, his mind taxed, searched frantically for a dictionary.
Nominative absolute: his mind taxed
With a verb added: His mind was taxed.
Similarly, one can break the absolute off, add a verb and make two sentences. For example, Stephen searched frantically for a dictionary. His mind was taxed.