Name and rules of this construction: "A somber man privately, Johnson had an acid humor."

Solution 1:

First, you shouldn't start with apposition; apposition is not a starting place, but the result of relative clause pruning.

• My son the doctor is coming for dinner = My son, who is a doctor, is coming for dinner.

In the case of the construction you ask about, it's not a relative clause that's being pruned, but an adverbial subordinate clause. A starting point for Eccentric and egotistical ... (with parenthesized material pruned) might be

• (Because/Although/While/Similarly,/<Subordinating conjunction>
  • Berkeley is/was) eccentric and egotistical, ...

This is rather like participial constructions, except the only verb in sight is the predicate adjective auxiliary be, which is totally predictable and therefore deleted, along with the equally predictable subject, leaving only the adjectives, but keeping the clausal intonation (whence the comma), and leaving the conjunction unspecified.

And giving rise to "dangling participles" like

Sitting on the fence, my mother saw three cats fighting.

As you suspect, the identity of the conjunction that would be appropriate is up to the listener to calculate from (their knowledge of (the speaker's knowledge of)) the context. So if you can't guess what connection might exist between being eccentric and egotistical, on the one hand, and having an interest in camera movement on the other, then for sure you might not be able to see what the speaker's getting at.

This kind of calculation is Pragmatic -- situational, dependent on the goals and effects of speech -- and not a part of a syntactic construction, or even semantics. It's all inference, though there are some guidelines.